Question

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A train covered a certain distance at a uniform speed if the train would have been 10 km per hour faster it would have take 2 hour less than the scheduled time if the train was slower by 10 km per hour it would have take 3 hour more than the scheduled time then the distance covered by a train is

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Answer 1

Answer:

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A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train

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• Find the distance covered by the train

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• We will be using the concept of two-variable linear equations to solve the given question.
• Let us assume the uniform speed of the train to be x km/h and the time taken to travel the given distance be t hours.
• Then distance can be calculated as follows:

$\tt{\implies}{ \boxed{\mathbb{\blue{Distance = speed × time = xt}}}}$

Thus, the distance is xt

According to the question,

Condition 1: When the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time.

(x + 10)(t - 2) = xt

xt - 2x + 10t - 20 = xt

- 2x + 10t = 20 ....(1)

Condition 2: When the train would have been slower by 10 km/h, it would have taken 3 hours more than the scheduled time.

(x - 10)(t + 3) = xt

xt + 3x - 10t - 30 = xt

3x -10t = 30 ....(2)

Adding equations (1) and (2), we obtain

- 2x + 10t + 3x -10t = 20 + 30

x = 50

Substituting x = 50 in equation (1), we obtain

- 2 × 50 + 10t = 20

- 100 + 10t = 20

10t = 120

t = 120/10

t = 12

Therefore, distance = xt = 50 × 12 = 600

$</p><p>\tt{\implies}{ \boxed{\mathbb{\purple{Hence, \: the \: distance \: covered by \: the \: train \: is \: 600 \: km.}}}}$

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