Solve the problem.
-A jet plane traveling at a constant speed goes 1200 miles with the wind, then turns around and travels for 1000 miles against the wind. If the speed of the wind is $50 \mathrm{mph}$ and the total flight took 4 hours, find the speed of the plane.
A) $525 \mathrm{mph}$
B) $605 \mathrm{mph}$
C) $550 \mathrm{mph}$
D) $435 \mathrm{mph}$

Question

Quizplus · Accepted Answer

Let the speed of the plane in still air be $x$ mph. With the wind, the plane's speed is $x + 50$ mph, and against the wind, it's $x - 50$ mph. The time to go 1200 miles with the wind is $\frac{1200}{x + 50}$ hours, and the time to go 1000 miles against the wind is $\frac{1000}{x - 50}$ hours. The total time is 4 hours, so we have the equation $\frac{1200}{x + 50} + \frac{1000}{x - 50} = 4$. Solving this equation for $x$ gives $x = 550$ mph.

Solve the Problem 50mph50 \mathrm{mph}50mph And the Total Flight Took 4 Hours, Find the Speed

Solve the Problem $50 \mathrm{mph}$ And the Total Flight Took 4 Hours, Find the Speed