Question

If a train runs at 40 kmph it reaches its destination late by 11 minutes. But if it runs
at 50 kmph it is late by 5 minutes only. Find the distance to be covered by the train.​

Answer 1

Answer:

Step-by-step explanation:

Given :

Speed of train is  and its late by 11 min or  .

In other case it's also given speed of train is  and late by 5 min or .

Let the train covered 'd' km distance.

The journey let it took 't' hr time.

We have difference in late of time i.e.

We know ,

A.T.Q.

d=20km

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Answer 2

Step-by-step explanation:

Let the normal time be ‘t’ hours to reach the destination at a distance of ‘x’ km

If the train runs at 40 km/hr it reaches the destination , the train is late by 11 minutes , i.e late by 11/60 hours, Ot it takes t + 11/60 hours. Then

Distance = Speed x time

i . e x = 40 *(t+11/60) ……….(1)

Again when the train runs at a speed of 50 km/he , it reaches 5 minutes late. So we have the following equation as well

i.e. x = 50 * ( t+ 5/60) …………. (2)

Equating equation (1) and (2), now we have this expression

40*(t+11/60) = 50(t+5/60)

4(t+11/60) = 5(t+5/60)

4t + 11/15 = 5t + 5/12

t = 11/15 - 5/12

t = (132 - 75)/180

t = 57/180

t = (57/180)*60 minutes

t = 19 minutes

If it runs at 40 km per hour , it reaches late by 11 minutes , i.e., it takes 19+11 = 30 minutes which means 30/60 = 1/2 hour .

Therefore x = 40*(1/2 )= 20 kms

Hence normal speed is 20/(19/60) = 63.15789 km/hr

Hence at a speed of 63.15789 km/hr, the train will reach the destination in 19 minutes

( at 40 km/hr the train will reach in 19+11 = 30 minutes , and at 50km/hr , the train will reach in 19+5 = 24 minutes)

Hence , the normal time without being late is 19 minutes