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rate of planes flying in opposite directions at different speeds

Two airplanes leave the airport at the same time, traveling in opposite directions. One plane travels 30 mph faster than the other. After 3 hours, the planes are 3150 miles apart. What is the rate of each plane?

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Roman C. | Masters of Education Graduate with Mathematics ExpertiseMasters of Education Graduate with Mathe...
4.9 4.9 (364 lesson ratings) (364)

Let x mph and x+30 mph be the speeds of the planes. The rate at which their distance from each other increases will be the sum of their speeds which is 2x+30 mph.

Their distance from each other after three hours is (3 hours)*(2x+30 mph) = 6x+90 miles. We are given that this is 3150 miles so we can solve for x.

6x+90 = 3150

6x = 3060

x = 510

Thus the speeds of the two planes are 510 mph and 540 mph.

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)

x = the slower rate

x+30 = the faster rate

Since the travelled in the opposite direction,

3(x+x+30) = 3150

Solve for x,

x = 510 mph

x+30 = 540 mph