Question

Bill's airplane has a cruising speed that is 30mph faster than Susan's airplane. Bill's airplane cruises a distance of 800 miles. In the same time, Susan's Airplane cruised a distance of 760 miles. What is the cruising speed of bill's airplane?

Answer 1

The answer is 600m/s. Hope it helps

Answer 2

600m/s

Explanation:

Step 1

First step is to use declare variables for Bill's and Susan's cruising speed.Let
`x` the speed of Susan's plane. This implies that Bill's plane is
`x+30`

Step 2

To calculate the time traveled given distance and speed we use the formula

`t=(d)/(s)` where
`s` is speed,
`d` is the distance,
`t` is the time.

The time taken by Bill's plane is
`t_b=(800)/(x+30).`

The time taken by Susan's plane is
`t_s=(760)/(x)`

Step 3

Since the time taken by both planes is the same, we solve for Susan's speed as shown below,

`t_b=t_s\\\implies (800)/(x+30) =(760)/(x) \\\implies 800x=760(x+30)\\\implies 800x=760x+22\,800\\\implies 800x-760x=22\,800\\\implies 40x=22\,800\\\implies x=(22\,800)/(40) =570`

Step 4

Since Susan's plane travels at a speed of 570mph, we can inder that Bill's plane travels at a speed of (570+30)mph=600mph.