Question

A student travels from CT to a tropical island in his family's plane. It took 20 hours to flythere and 24 hours to fly back home. What is the wind speed if in still air his plane flies120 mph? Set up an equation and show all work. Round to the nearest tenth if necessary.(4pts)

Answer 1

10.9 mph

Step-by-step explanation:

Let's call x the wind speed and y the distance traveled from CT to a tropical island.

The distance traveled is equal to the resultant speed times the time, so if it took 20 hours to fly there, we can write the followin equation

y = (120 + x)20

Because (120 + x) is the resultant speed, it is the speed of the plane less the speed of the wind, and 20 is the time this travel takes.

In th same way, it took 24 hours to fly back home, so

y = (120 - x)(24)

Since the distance traveled is the same, we can write the following equation

(120 + x)20 = (120 - x)(24)

Solving for x, we get:

120(20) + x(20) = 120(24) - x(24)

2400 + 20x = 2880 - 24x

2400 + 20x + 24x = 2880 -24x + 24x

2400 + 44x = 2880

2400 + 44x - 2400 = 2880 - 2400

44x = 480

44x/44 = 480/44

x = 10.9

Therefore, the wind speed is 10.9 mph