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