Two planes start from the same point and fly in opposite directions. The first plane is flying 30 mph slower than the second plane. In 3 h, the planes are 810 mi apart. Find the rate of each plane.

Given two planes flying in opposite directions are 810 miles apart after 3 hours, and the first is 30 mph slower than the second, you want the speed of each plane.

Setup

Let s represent the speed of the slower plane. Then faster plane will have a speed of (s+30). The distance between the planes increases at a rate equal to the sum of their speeds. Distance is the product of speed and time, so we have ...

distance = speed × time

810 = (s + (s+30)) × 3

Solution

Dividing the equation by 3, we get ...

270 = 2s +30

240 = 2s . . . . . . subtract 30

120 = s . . . . . . . divide by 2

150 = s+30 . . . the speed of the faster plane

The speed of the first plane is 120 mph; the speed of the second plane is 150 mph.

ogorwyne ogorwyne · Answer 2 · 2022-10-14T13:41:19-04:00

The rate of the two planes flying in opposite direction was found to be

The faster plane = 150 mph

The slower plane = 120 mph

How to find the rate of each plane

given data

The first plane is flying 30 mph slower than the second plane.

time = 3 hours

distance = 810 miles

let the rate of the faster plane be x

then rate if the slower plane will be x - 3

rate of both planes

= x + x - 30

= 2x - 30

Finding the rate of each plane

rate of both planes = total distance / total time

2x - 30 = 810 / 3

2x - 30 = 270

2x = 270 + 30

2x = 300

x = 150

Then the slower plane = 150 - 30 = 120 mph

Hence the rate of the faster plane is 150 mph and the rate of the slower plane is 120 mph

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