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.

Speed is equal to the distance traveled divided by time.

Answer: The distance covered by the train will be 600 km.

Let's find the distance covered by the train.

Explanation:

Let's consider the time taken to be 't'

Let the speed be 'x' and distance be 'd'

Distance = Speed × Time

By substituting in the above equation we get,

d = xt ----------------- (1)

Case 1: When speed is increased by 10 km/h and time is decreased by 2 hours.

New speed = x + 10, New time = t - 2

Substituting the values we get,

d = (x + 10)(t – 2) 

d = xt – 2x + 10t - 20

d = d – 2x + 10t - 20 [since, d = xt from equation (1)]

10t – 2x = 20 ---------------------- (2)

Case 2: When speed is reduced by 10 km/h, time increases by 3 hours.

New speed = x - 10, New time = t + 3

Substituting the values we get,

d = (x – 10)(t + 3) 

d = xt + 3x -10t – 30

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

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

Adding equation (2) and (3)

10t - 2x + 3x -10t = 20 + 30

x = 50

To calculate the value of time, substitute the value of x in equation (2)

10t – (2 × 50) = 20

10t = 20 + 100

10t = 120

t = 12 hours

Now, to calculate the distance, substitute the value of t and x in equation (1)

d = xt

d = 50 × 12

d = 600 km

Thus, the distance covered by the train is 600 km.