Two planes are 2300 mi apart and are traveling toward each other. One plane is traveling 120 mph faster than the other plane. The planes pass each other in 2.5 h. Find the speed of each plane.

Question

Two planes are 2300 mi apart and are traveling toward each other. One plane is traveling 120 mph faster than the other plane. The planes pass each other in 2.5 h. Find the speed of each plane.

Answer 1

let's say we have two planes, plane1 and plane2

plane1 travels at a rate r1

plane2 travels at a rate r2, which is 120 more than plane1, therefore r2 = r1+120

each plane travels for 2.5hrs until they meet, since distance = rate x time, the distance each plane travels is...

d1 = r1*2.5

d2 = r2*2.5 = (r1+120)*2.5

the total distance the planes travel is 2300mi, so the sum of their distances traveled equals 2300...

d1 + d2 = 2300

now we can substitute our formulas for d1 and d2 into this equation and solve for r1...

d1 + d2 = 2300

2.5r1 + 2.5(r1+120) = 2300

2.5r1 + 2.5r1 + 300 = 2300

5r1 = 2000

r1 = 400mph

r2 = 400 + 120 = 520mph