Question

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

Answer 1

Let us consider the time of journey be T hrs

then,as distance is same, then

A/Q,

⇒40( T +11/60) =50 (T- 5/60)

⇒T= 23/30 hr

distance= speed ×time

              = 40×23/30

              =92/3 km

              =30.66 km

Answer 2

Let x be the constant duration.

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STEP 1: Find distance for the train that runs at 40kmph,

The train travels at 40km/h

The train is 11 mins late

⇒ duration = x + 11/60 hours

.

Distance = Speed x Time

Distance = 40(x + 11/60)

Distance = (40x + 22/3) km

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STEP 2: Find distance for the train runs at 50kmph:

The train travels at 50 km/h

The train is 5 mins late

⇒ duration = x + 5/60 hours

⇒ duration = x + 1/12 hours

.

Distance = Speed x Times

Distance = 50(x + 1/12)

Distance = (50x + 25/6) km

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STEP 3: Find x:

Since both the travel the same distance:

40x + 22/3 = 50x + 25/6

50x - 40x = 22/3 - 25/6

10x = 19/6

x = 19/60

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STEP 4: Find distance:

Distance = 40x + 22/3

Distance = 40(19/60) + 22/3

Distance = 20 km

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Answer: The distance is 20 km