SOLUTION: Two Air Force planes, one a jet and the other propeller-driven plane, left an air base at the same time and flew to another base 600 miles away. The jet's average speed was 300 mil

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Question 181929: Two Air Force planes, one a jet and the other propeller-driven plane, left an air base at the same time and flew to another base 600 miles away. The jet's average speed was 300 miles per hour greater than that of the propeller-driven plane and its flying time was 2 and 2/3 hours less. Find the average speed of each plane.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two Air Force planes, one a jet and the other propeller-driven plane, left an
air base at the same time and flew to another base 600 miles away.
The jet's average speed was 300 miles per hour greater than that of the
propeller-driven plane and its flying time was 2 and 2/3 hours less.
Find the average speed of each plane.
:
Let s = speed of the prop plane
then
(s+300) = speed of the jet plane
:
Write a time equation; time = dist%2Fspeed
Prop time - jet time = 22%2F3 hrs
:
600%2Fs -600%2F%28%28s%2B300%29%29 = 8%2F3
:
Multiply equation by 3s(s+300) to get rid of those annoying denominators
600*3(s+300) - 600*3s = 8s(s+300)
:
1800s + 540000 - 1800s = 8s^2 + 2400s
:
do the math and arrange as a quadratic equation
8s^2 + 2400s - 540000 = 0
;
simplify, divide by 8
s^2 + 300s - 67500 = 0
:
With a little sweat we can get this to factor
(s + 450) (s - 150) = 0
the positive solution:
s = +150 mph is the prop plane
:
I'll let you find the jet plane speed
:
:
Check solution in original equation