Question

A plane averaged 800 mph on a trip going​ east, but only 400 mph on the return trip. The total flying time in both directions was 4.5 hr. What was the​ one-way distance?

Answer 1

1200 miles.

Explanation:

Let d represent one way distance.

We have been given that a plane averaged 800 mph on a trip going​ east, but only 400 mph on the return trip.

`\text{Time}=\frac{\text{Distance}}{\text{Speed}}`

The time taken while going east would be
`(d)/(800)`.

The time taken while returning back would be
`(d)/(400)`.

Since the total flying time in both directions was 4.5 hr, so we will equate sum of both times with 4.5 as:

`(d)/(800)+(d)/(400)=4.5`

Make a common denominator:

`(d)/(800)+(d*2)/(400*2)=4.5`

`(d)/(800)+(2d)/(800)=4.5`

`(d+2d)/(800)=4.5`

`(3d)/(800)=4.5`

`(3d)/(800)* (800)/(3)=4.5* (800)/(3)`

`d=1.5* (800)/(1)`

`d=1200`

Therefore, the one-way distance was 1200 miles.