solving a distance, rate, time problem using a rational equation

Question

A plane has a cruising speed of 

200

miles per hour when there is no wind. At this speed, the plane flew

500

miles with the wind in the same amount of time it flew 

300

miles against the wind. Find the speed of the wind.

Answer 1

Here's another approach:

d = rt, so t = d/r

Both trips took the same time

r with wind is p + w; r against wind is p - w. p = 200 mph

500/(200 + w) = 300/(200 - w)

Cross-multiply: 60000 + 300w = 100000 - 500w

800w = 40000 → w = 50 mph.

Answer 2

500 miles with the wind

300 miles against the wind

let w = wind, p = plane

distance = rate of speed times time

d =rt

500 = p+w

300 = p-w

add the equations

2p = 800

p = 400 miles without wind, at 200 mph that's 2 hours

in 2 hours the plane went 500 with the wind

in 2 hours the plane went 300 against the wind

the wind was 50 mph, the plane 200 mph

in 2 hours with the wind the plane went 500 miles = (200+50)(2) =250(2)=500

in 2 hours against the wind the plane went 300 miles = (200-50)(2) = 150(2) = 300