Question

A pilot fl ew a small plane 525 miles from Houston, Texas, to Pensacola, Florida, in 3 hours against the wind. The pilot returned to Houston in 2 hours and 30 minutes with the wind at the plane’s tail. How fast was the plane fl ying without the wind? What was the speed of the wind?

Answer 1

The plane speed without wind is 192.5 mph, and the wind speed is 17.5 mph, which were calculated using the distance formula and setting up a system of equations with the given flight data.

Step-by-step explanation:

To determine the speed of the small plane without wind and the speed of the wind, we need to establish two equations using the given information:

• • The plane flew 525 miles from Houston to Pensacola against the wind in 3 hours.
  • The return trip from Pensacola to Houston with the wind at the plane’s tail took 2 hours and 30 minutes (or 2.5 hours).

Let's denote plane speed (in still air) by 'p' and wind speed by 'w'. When flying against the wind, the effective speed is (p - w), and with the wind, the effective speed is (p + w).

Using the distance formula (distance = speed × time), we can set up the following equations:

1. 1. 525 = (p - w) × 3 (against the wind)
   2. 525 = (p + w) × 2.5 (with the wind)
2. Divide both sides of each equation to isolate (p - w) and (p + w):

1. 1. 175 = p - w
   2. 210 = p + w
2. Add these two equations to eliminate 'w':

175 + 210 = p - w + p + w

385 = 2p

Divide by 2 to find the plane's speed without wind:

p = 192.5 mph

Now, we can substitute the value of 'p' back into either of the original equations to find 'w'. Using the first equation:

175 = 192.5 - w

w = 192.5 - 175

w = 17.5 mph

Therefore, the plane speed without wind is 192.5 mph, and the wind speed is 17.5 mph.