Question

1. it takes a plane 3.5 hours to fly 2,345 miles and 2 hours to fly 860 miles going the opposite direction along the same route.

a. how fast does the plane fly during the first leg of the trip?
b. how fast does the plane fly during the last leg of the trip?
c. what system of equations might be helpful in this scenario?

Explanation:

Step1: Calculate first leg speed

$\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2345}{3.5}$

Step2: Compute first leg value

$2345 \div 3.5 = 670$

Step3: Calculate last leg speed

$\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{860}{2}$

Step4: Compute last leg value

$860 \div 2 = 430$

Step5: Define variables for equations

Let $p$ = plane's airspeed, $w$ = wind speed

Step6: Set up first leg equation

With wind: $p + w = \frac{2345}{3.5} = 670$

Step7: Set up last leg equation

Against wind: $p - w = \frac{860}{2} = 430$

Answer:

a. 670 miles per hour
b. 430 miles per hour
c.

$$\begin{cases} p + w = 670 \\ p - w = 430 \end{cases}$$

where $p$ is the plane's airspeed in miles per hour, and $w$ is the wind speed in miles per hour.