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

Answer:

1200 miles.

Step-by-step 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 $\frac{d}{800}$.

The time taken while returning back would be $\frac{d}{400}$.

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

$\frac{d}{800}+\frac{d}{400}=4.5$

Make a common denominator:

$\frac{d}{800}+\frac{d*2}{400*2}=4.5$

$\frac{d}{800}+\frac{2d}{800}=4.5$

$\frac{d+2d}{800}=4.5$

$\frac{3d}{800}=4.5$

$\frac{3d}{800}\times \frac{800}{3}=4.5\times \frac{800}{3}$

$d=1.5\times \frac{800}{1}$

$d=1200$

Therefore, the one-way distance was 1200 miles.