Question

A train covered a certain distance at a uniform speed. If the train had been 5 kmph faster, it would have taken 3 hours less than the scheduled time. And, if the train were slower by 4 kmph, it would have taken 3 hours more than the scheduled time. Find the length of the journey.

Answer 1

Let the original speed be x kmph and let the time taken to complete the journey be y hours.

∴ Length of the whole journey = (xy) km

Case I:

When the speed is (x + 5) kmph and the time taken is (y – 3) hrs:

Total journey = (x + 5) (y – 3) km

⇒ (x + 5) (y – 3) = xy

⇒ xy + 5y – 3x – 15 = xy

⇒ 5y – 3x = 15   ...(i)

Case II:

When the speed is (x – 4) kmph and the time taken is (y + 3) hrs:

Total journey = (x – 4) (y + 3) km

⇒ (x – 4) (y + 3) = xy

⇒ xy – 4y + 3x – 12 = xy

⇒ 3x – 4y = 12   ...(ii)

On adding (i) and (ii), we get:

y = 27
On substituting y = 27 in (i), we get:

5 × 27 – 3x = 15

⇒ 135 – 3x = 15

⇒ 3x = 120

⇒ x = 40

∴ Length of the journey = (xy) km

= (40 × 27) km

= 1080 km