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

Answer:

600m/s

Step-by-step 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

$t=\frac{d}{s}$  where $s$ is speed, $d$ is the distance, $t$ is the time.

The time taken by Bill's plane is $t_b=\frac{800}{x+30}.$

The time taken by Susan's plane is $t_s=\frac{760}{x}$

Step 3

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

$t_b=t_s\\\implies \frac{800}{x+30} =\frac{760}{x} \\\implies 800x=760(x+30)\\\implies 800x=760x+22\,800\\\implies 800x-760x=22\,800\\\implies 40x=22\,800\\\implies x=\frac{22\,800}{40} =570$

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.

Answer 2

Answer:

The answer is 600m/s. Hope it helps