Question

if a train runs at 40kmph 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. please answer this question with explanation​

Answer 1

$\huge\star\:\:{\orange{\underline{\pink{\mathbf{Answer}}}}}$

$\large\bold{\underline{\sf{\purple{Given}}}}$

If a train runs at 40 km/hr it reaches it's destination late by 11 minutes

If it runs at 50 km/hr it is late by 5 minutes

$\large\bold{\underline{\sf{\orange{To\:Find}}}}$

The distance to be covered by the train.

$\large\bold{\underline{\sf{\pink{Solution}}}}$

Let train take x hr to reach the destination.

11 minute = 11/60 hr and

5 minute = 5/60 hr

Distance = Time × Speed

It's late means it take more time than the required time.

According to the first condition.

Distance = ( x + 11/60 ) × 40

=> Distance = 40x + 22/3...(1)

According to the second condition.

Distance = ( x + 5/60 ) × 50

=> Distance = 50x + 25/6...(2)

From equation (1) and (2), we get

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

=> 10x = 22/3 - 25/6

=> 10x = (44-25)/6

=> 10x = 19/6

=> x = 19/60

Substituting in equation (1), we get

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

=> Distance = 38/3 + 22/3

=> Distance = 60/3

=> Distance = 20 km

The distance to be covered by the

train is 20 km

$\huge\underline\bold\green{Thanks}$

Answer 2

Step-by-step explanation:

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

.....................................................................................................................

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

.....................................................................................................................

Answer: The distance is 20 km