Question

QUESTION:-

A train covered a certain distance at a uniform speed.If the train have been 10km/h faster,it would have taken 2hrs less than the scheduled time.And,if the train was slower by 10km/h ,it would have taken3 hrs more than the scheduled time.Find the distance covered by the train.​

Answer 1

See below.

Explanation:

Let us consider,

Time is taken = t

Speed = x

Distance = d

Time = Distance/Speed

or

Speed = Distance/time

x = d/t

d=xt...(1)

Condition 1:

d = (x + 10)(t – 2)

d = xt – 2x +10t -20

d = d – 2x +10t -20 [from (1) xt = d]

10t – 2x = 20...(2)

Condition 2:

d = (x – 10)(t + 3)

d = xt + 3x -10t – 30

d = d + 3x -10t – 30 [from (1) xt = d]

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

Adding equations [(2) and (3)]

(10t – 2x + 3x -10t) = 20 + 30

x = 50

Substituting the value of x in 2

10t – 2 × 50 = 20

=>10t = 100 + 20

=>10t = 120

=>t = 12 hrs

Now substitute the value of t and in x in equation (1):

We know,Distance d = xt

=>d = 50 × 12

=>d = 600 km

• Hence, distance covered by the train is 600km.