Question

Solve by using methods of factoring, the square root principle, or the quadratic formula. Round your answer to the nearest tenth. The couple took a small airplane for a quick flight up to the wine country for a romantic dinner and then returned home. The plane flew a total of 6 hours and each way the trip was 400 miles. If the plane was flying at 150 mph, what was the speed of the wind (in mph) that affected the plane?

Answer 1

50 mph

Explanation:

You want the speed of the wind such that a trip of 400 miles and back took 6 hours in a plane flying 150 mph relative to the wind.

Time

The relation between time, speed, and distance is ...

time = distance/speed

The speed in one direction is assumed to be with the wind, and in the other direction, against the wind. The total time for the two trips is ...

6 h = (400 mi)/(150 +w mi/h) +(400 mi)/(150 -w mi/h)

Solution

The units match, so we can drop them. Multiplying by (150+w)(150-w), we have ...

6(150 +w)(150 -w) = 400((150 +w) +(150 -w))

150² -w² = 400(50) . . . . . . . . . simplify, divide by 6

150² -400(50) = w²

w = √2500 = 50

The speed of the wind was 50 miles per hour.