SOLUTION: Plane 1 can travel 1400 miles in 1 hour less time than it tales plane B to travel 2000 miles. The rate of plane B is 50 miles per hour greater than the rate of plane A. Find the ti

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Question 287285: Plane 1 can travel 1400 miles in 1 hour less time than it tales plane B to travel 2000 miles. The rate of plane B is 50 miles per hour greater than the rate of plane A. Find the times and rates of both planes.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Plane 1 can travel 1400 miles in 1 hour less time than it tales plane B to travel 2000 miles.
The rate of plane B is 50 miles per hour greater than the rate of plane A.
Find the times and rates of both planes.
:
Let r = the rate of plane A
then
(r+50) = the rate of plane B
;
Write a time equation, Time = dist/rate
:
Plane B time - Plane A time = 1 hr
2000%2F%28%28r%2B50%29%29 - 1400%2Fr = 1
Multiply by r(r+50); results
:
2000r - 1400(r+50) = r(r+50)
:
2000r - 1400r - 70000 = r^2 + 50r
:
600r - 70000 = r^2 + 50
Arrange as a quadratic equation
0 = r^2 + 50r - 600r + 70000
:
r^2 - 550r + 70000 = 0
Factor
(r - 350)(r - 200) = 0
Two solutions
r = 200 mph for plane A; then 250 mph for plane B
and
r = 350 mph for plane A; then 400 mph for plane B
:
Both these solutions will work
:
Find the times when Plane A = 200 mph
B: 2000/250 = 8 hr
A: 1400/200 = 7 hr
:
find the times when Plane A = 350 mph
B: 2000/400 = 5 hr
A: 1400/350 = 4 hr