Solve Applications Involving Uniform Motion

Question

Two planes leave from Atlanta, Georgia. One makes a 5.2-hr flight to Seattle, Washington, and the other makes a 2.5-hr flight to Boston, Massachusetts. The plane to Boston averages 44 mph slower than the plane to Seattle. If the total distance traveled by both planes is 3124 mi, determine the average speed of each plane.

Answer 1

5.2s + 2.5b = 3124

s=44+b

5.2(44+b) +2.5b = 3124

5.2b + 2.5b = 3124 -5.2(44)

7.7b = 3124- 228.8 = 2895.2

b = 2895.2/7.7 = 376 mph for boston plane

s = 376+44 = 420 mph for seatle bound plane

check the answer:

5.2 hours times 420 mph = 2184 miles

2.5 hours times 376 mph = 940 miles

2184+940 = 3124 total miles for both planes