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Mathematics for LGO Examination

Time and Distance

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Compiled by
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R.Hariharakrishnan
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Manager,
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Postal Stores Depot,

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Tirunelveli 627002
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Suggestions towards improvement are always welcome.

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Time and Distance

1. To convert KMPH into meter/sec, multiply by 5/18

2. To convert meter/sec to KMPH multiply by 18/5
3. 1 KM=1000 meters.
4. 1 KMPH means 1KM/1 hour=1000 m/1 hour=1000 m/60 minutes=1000 m/3600 sec
5. Time=(distance/speed); speed=(distance/time);
6. Speed is the distance covered in one hour or 3600 seconds.

Let us see some examples.

Example 1:

How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hour.

Solution:

20 KMPH =20*(5/18)=50/9 m/sec

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Time taken to cover 400 m=(400)/(50/9)=3600/50=72 sec

Another method
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20 KMPH means 20000 meter in 1 hour. 20000 m in 3600 sec.

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Time taken to cover a distance of 20000 m is 3600 sec.

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Time taken to cover a distance of 400 m is (3600/20000)*400=72 seconds

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Example2:
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A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in KMPH. Of the cyclist.

Solution:

Speed=(750/150) m/sec=5 m/sec.=5*(18/5) kmph. =18 KMPH.

Another method:

To find the distance covered in 1 hour and convert to KMPH.

Distance covered in 2 min and 30 sec (150 sec)=750 m

Distance covered in 3600 seconds=(750/150)*3600=18000 meter in 3600 seconds. i.e.18 KMPH.

Example 3:

An aeroplane flies along the four sides of a square at the speeds of 200,400,600 and 800 KMPH. Find the
average speed of the plane around the field.
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Solution:

Note: Square field means all the four sides are equal.

Let the length of each side=x

Time taken to cover each side of the field.

Side 1 at 200 KMPH= x/200

Side 2 at 400 KMPH=x/400

Side 3 at 600 KMPH=x/600

Side 4 at 800 KMPH=x/800

Total distance=4*x

Total time=(x/200)+(x/400)+(x/600)+(x/800)=(12x+6x+4x+3x)/2400 (LCM of 200,400,600,800 is 2400)

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25x/2400
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Average speed=total distance/total time=(4x)/(25x/2400)=(2400*4)/25=384 KMPH.
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Another method (simple method)

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Let each side of the square=2400 (LCM of 200,400,600,800 is 2400)

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Time taken for side 1=2400/200=12 hours

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Time taken for side 2=2400/400=6 hours

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Time taken for side 3=2400/600=4 hours

Time taken for side 4=2400/800=3 hours

Total distance=4*2400=9600 KM

Total time taken=12+6+4+3=25 hours

Average speed=9600/25=384 KMPH.

Example 4:

Running at 5/6 of its usual speed, a train is 10 minutes too late. Find its usual time to cover the journey.

Solution:

New speed=(5/6) of uslal speed

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New time taken=(6/5) of usual time.

Given the time difference is 10 minutes.

(6/5 of usual time)-(usual time)=10 minutes

{ (6/5)-1} of usual time=10 minutes..

1/5 th of usual time=10 minutes.

Usual time=10*(5/1)=50 minutes.

Another method (shortcut and easy method)

Note: we have to find 5/6 of usual speed. Hence take the speed as 60 which is divisible by 6. You can
take any number divisible by 60. If the usual speed is 60 then 5/6 th speed is 50 KMPH. Hence take the
total distance as a number divisible by 50 and 60. Here I take it as 600 KM.

Let the distance=600 km

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Let the usual speed=60 KMPH
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Usual time=600/60=10 hours.
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Revised speed=(5/6)*60=50 KMPH

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Revised time=600/50=12 hours.

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Difference in time=2 hours.

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If difference in time is 120 minutes then usual time=600 minutes.

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If difference in time is 10 minutes then usual time=(600/120)*10=50 minutes.

Example 5:

If a man walks at the rate of 5 KMPH he misses the train by 7 minutes. However, if he walks at the rate
of 6 KMPH, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by
him to reach the station.

Solution:

Note: We can use the method used in the previous problem.

Let the distance of the station=30 KM (divisible by 5 KMPH and 6 KMPH)

Time taken at 5KMPH=(30/5)=6 hours

Time taken at 6 KMPH=(30/6)=5 hours

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Difference =1 hour=60 minutes.

If the difference in time is 60 minutes the distance is 30 KM

If the difference in time is 10 minutes the distance is (30/60)*12=6 KM ***

*** AT 5 KMPH he arrives late by 7 minutes and at 6 KMPH he arrives 5 minutes in advance. The time
difference is 7+5=12 minutes.

Example 6:

A and B are two stations 390 KMs apart. A train starts from A at 10 AM and travels towards B at 65
KMPH. Another train starts from B at 11 AM and travels towards A at 35KMPH. At what time do they
meet.

Solution:

Let they meet X hours after 10 AM.

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Distance travelled by first train at 65 KMPH for x hours+distance travelled by second train in (x-1) hours
at 35 KMPH=390 KM
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65x+35(x-1)=390
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65x+35x-35=390
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100x=390+35=425
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X=4 ¼ hours
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The trains will meet 4 ¼ hours after 10 AM i.e. 2.15 PM

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Another method (easy method)

Important notes:

Time=(distance/speed)

In these type of sums, distance means the distance between the trains when the second train starts.

Speed means relative speed. If the trains are going in the same direction, relative speed is the difference
of speeds. If the trains are coming in opposite directions, relative speed is the sum of the speeds.

Use Time=(distance/speed) to find the time after the trains will meet.

This should be added to the time at which the second train starts.
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The second train starts at 11 AM. At this time, the first train crossed 65 KM at 11 AM.

Distance between the trains at 11 AM=390-65=325 KM

The trains are travelling in opposite directions. Relative speed=65+35=100 KMPH

Time=325/100=3.25=3 ¼ hours.

This should be added to 11 AM. The time of meeting=2.15 PM

Example 7:

A train covers a distance of 10 KM in 12 minutes. If its speed is decreased by 5 KMPH, the time taken by
it to cover the same distance will be.

Solution:

Distance covered by the train in 12 minutes=10 KM

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Speed is the distance covered in 1 hour=60 minutes=50 KMPH.

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If the speed is reduced by 5 KMPH, the revised speed=45 KMPH t.c
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Time taken to cover 10 KM at 45 KMPH=(10/45) hour=(10*60)/45 minutes=13 min 20 sec
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Example 8:
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A boy goes to his school from his house at a speed of 3 KMPH and returns at a speed of 2 KMPH. If he
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takes 5 hours in going and coming, find the distance between his house and school.
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Solution:
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Let the distance between the house and school= 6 KM (divisible by 3 and 2)

Time from house to school at 3 KMPH=6/3=2 hours

Time from school to house at 2 KMPH=6/2=3 hours

Total time= 5 hours.

The distance between house and school=6 KM.

Note: If the time is given as 1 hour instead of 5 hours.

If the time is 5 hours then the distance is 6 KM

If the time is 1 hour then the distance is (6/5)*1=1.5 KM

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Example 9:

A person covers a distance of 12 KM while walking at a speed of 4 KMPH. How much distance he would
cover in same time, if he walks at a speed of 6 KMPH?

Solution:

If the speed is 4 KMPH the distance covered is 12 KM

If the speed is 6 KMPH the distance covered is (12/4)*6=18 KM

Example 10:

A person covers a certain distance with a speed of 18 KMPH in 8 minutes. If he wants to cover the same
distance in 6 minutes, what should be his speed?

Solution:

18 KMPH means 18000/60=300 m/minute

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Distance covered in 8 minutes at 18 KMPH=8*300=2400 m
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To cover 2400 m in 6 minutes, his speed is 2400/6=400 m/minute
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Speed is=400*60=24000 m/hour=24 KMPH.

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Problems for practice.

1. A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express
train leave the same station and moves in the same direction at a uniform speed of 90 KMPH.
This train catches the goods train in 4 hours. Find the speed of goods train.
2. An athlete runs 200 metres race in 24 seconds. His speed in KMPH is.
3. A person crosses a 600 m long street in 5 minutes. What is his speed in KMPH.
4. A man walking at the rate of 5 KMPH crosses a bridge in 15 minutes. The length of the bridge is
(in meters. )
5. How long will a boy take to run round a square field of side 35 Metres, if he runs at the rate of 9
KMPH.
6. A train travels at an average of 50 miles per hour for 2 ½ hours and then travels at a speed of 70
miles per hour for 1 ½ hours. The total distance travelled is.
7. An express train travelled at an average speed of 100 KMPH, stopping for 3 minutes after every
75 KM. How long did it take to reach its destination 600 KM from the starting point.
8. An aeroplane covers a certain distance at a speed of 240 KMPH in 5 hours. To cover the same

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distance in 1 2/3 hours,it must travel at a speed of …..KMPH

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9. A per travels equal distances with speeds of 3, 4, 5 KMPH and takes a total time of 47 minutes.
The total distance is t.c
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10. A boy rides his bicycle 10 KM at an average speed of 12 KMPH and again travels 12 KM at an
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average speed of 10 KMPH. His average speed for the entire trip is.
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11. A man travels 600 KM by train at 80 KMPH, 800 KM by ship at 40 KMPH, 500 KM by aeroplane at
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400 KMPH and 100 KM by car at 50 KMPH. What is the average speed for the entire journey.
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12. If a train runs at 40 KMPH, it reaches its destination late by 11 minutes but if it runs at 50 KMPH,
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it is late by 5 minutes only. The correct time for the train to complete the journey is.
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13. Two men start together to walk to a certain destination, one at 3 KMPH and another at 3.75
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KMPH. The latter arrives half an hour before the former. The distance is.
14. The distance between two cities A and B is 330 KM. A train starts from A at 8 AM and travels
towards B at 60 KMPH. Another train starts from B at 9 AM and travels towards A at 75 KMPH.
At what time do they meet.