Question

A train goes twice as fast downhill as it can go uphill, and 2/3 feet as fast uphill as it can go on level ground. If it goes 120 miles per hour downhill, how long will it take to travel 45 miles per flat

Answer 1

0.5hrs

Explanation:

Let the speed downhill be
`x`,

Speed uphill is
`0.5x`. We are told than speed uphill is
`(2)/(3)` the speed on flat ground. Therefore the speed on level ground will be
`(0.5x)/(2/3)=0.75x`.

From this info, we can obtain the actual speed,
`v_g` on level ground as:

`x=120m/h\\0.75x=v_g\\\\\therefore v_g=(0.75x * 120m/h)/(x)\\v_g=90m/h`

speed, distance and time have the relation
`s=d/t` so to obtain time to cover 45miles:

`t=d/s\\=45/90\\=0.5h`

Hence it takes 0.5hrs to cover 45miles on flat ground.