Question

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. Find the original speed of the train.

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.

Answer 1

Let the speed of the train = x km/hr

Total distance covered by the train = 480 km

∴ Time taken to cover the distance 480 km = `480/x` hr

If the speed has increased 8 km/hr, i.e., (x + 8) km/hr

Then, time taken to cover the distance 480 km = `480/(x - 8)` hr.

According to the question,

`480/(x - 8) - 480/x = 3`

⇒ `480 [(x - x + 8)/(x(x - 8))] = 3`

⇒ `8/(x^2 - 8x) = 3/480 = 1/160`

⇒ x² – 8x – 1280 = 0

Compare with ax² + bx + c = 0, we get a = 1, b = – 8 and c = –1280

∴ `x = (8 +- sqrt(64 + 4 xx 1280))/(2 xx 1)`

= `(8 +- sqrt(5184))/2`

= `(8 +- 72)/2`

= `(8 + 72)/2, (8 - 72)/2`

= `80/2, (-64)/2`

= 40, –32

Since, negative speed cannot be possible.

Hence, the original speed of the train = 40 km/ hr.