System of Equations Word Problems

Question

Flying against the jetstream, a jet travels 4250 miles in 5 hours. Flying with the jetstream, the same jet travels 9630 miles in 9 hours. What is the rate of the jet in still air and what is the rate of the jetstream?

Answer 1

9630 miles in 9 hours downstream

4250 miles in 5 hours up stream

distance = rate of speed times time, d=rt

9630 = (p+w)9

1070 = p+2

4250 = (p-w)5

850 = p-w

add the two equations

1070+850 = 2p

p = 1920/2 = 960 mph = plane speed in still air

w = p-850 = 110 mph = wind speed

upstream speed = 850 mph

downstream speed = 1070 mph

1070(9) = 9630 miles downstream

850(5) = 4250 miles upstream

Answer 2

First, we calculate the speed against the jetstream and the speed with the jetstream. Speed is distance divided by time, so the speed against the jetstream is 5250/5 = 850 mph. Flying with the jetstream the speed is 9630/9 = 1070 mph. Next, we need to realize that while flying with the wind the net speed is the sum of the jet and wind, but when flying into the wind the net speed is the difference between them. Let's use j for the jet's speed and w for the wind's speed. j + w = 1070 and j - w = 850. We now have a system of equation which is set up nicely for the elimination method. If we ADD the equations the w's cancel each other out and we get 2j = 1920. Dividing by 2 shows that j = 960. We can substitute 960 for the j in either of our equations and solve for w. Let's use the first equation, 960 + w = 1070. Subtract 960 from each side yields w = 110 mph. But don't forget to wrap up your answer as a sentence. "The jet's speed is 960 mph and the speed of the jetstream is 110 mph."