Distance, rate, time of planes

Two planes just took off from Boston, MA. The first plane is traveling 3 times as fast as the second plane. After traveling in the same direction for 2 hours, they are 396 miles apart. What is the average speed of each plane? (Hint: Since they are traveling in the same direction, the distance between them will be the difference of their distances.)

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distance = rate x time
d = rt

first plane
rate = 3r {three times the second plane’s rate}
time = 2 {2 hours}
d = 3r(2) {distance = rate x time}
d = 6r {multiplied}

second plane
rate = r
time = 2 {2 hours}
d = 2r {distance = rate x time}

6r - 2r = 396 {distance between them is difference in distances}
4r = 396 {combined like terms}
r = 99 mph {second plane’s rate}

3r is the first plane’s rate {taken from above}
3r = 3(99) = 297 mph {first plane’s rate}

first plane = 297 mph
​second plane = 99 mph

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