Question

A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train was slower by 6 km/h it would have taken 6 hours more than the scheduled time. Find the length of the journey.

Answer 1

Let the speed of the train be x km/hr.

Let the time taken to travel certain distance be y hrs.

We know that, speed × time = distance

∴ Distance = xy km

According to the first condition, if the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time.

∴ (x + 6)(y – 4) = xy

∴ xy – 4x + 6y – 24 = xy

∴ – 4x + 6y – 24 = 0

∴ 2x – 3y = –12     ......(i)

According to the second condition, if the train was slower by 6 km/hr, it would have taken 6 hours more than the scheduled time.

∴ (x – 6)(y + 6) = xy

∴ xy + 6x – 6y – 36 = xy

∴ 6x – 6y – 36 = 0

∴ x – y = 6   ......(ii)

Multiplying both sides by 2, we get

2x – 2y = 12   ......(iii)

Subtracting equation (iii) from (i), we get

2x – 3y = –12
2x – 2y = 12
–      +       –      
      – y = – 24

∴ y = 24

Substituting y = 24 in equation (ii), we get

x – 24 = 6

∴ x = 30

∴ Length of the journey = xy

= 30 × 24

= 720 km