SOLUTION: A jet plane traveling at 500 mph overtakes a propeller plane traveling 150 mph that had a 2 hr head start. How far from the starting point are planes? The Planes are ? miles fro

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Question 987623: A jet plane traveling at 500 mph overtakes a propeller plane traveling 150 mph that had a 2 hr head start. How far from the starting point are planes?
The Planes are ? miles from the starting point.
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A jet plane traveling at 500 mph overtakes a propeller plane traveling 150 mph that had a 2 hr head start.
How far from the starting point are planes?
:
let t = travel time of the jet
then
(t+2) = travel time of the prop
:
When the jet overtakes the prop, they will have traveled the same dist
Write a dist equation, dist = speed * time
500t = 150(t+2)
500t = 150t + 300
500t - 150t = 300
350t = 300
t = 300/350
t = .857 hrs travel time of the jet
Find the distance from the starting point
.857 * 500 = 428.6 mi
:
check this by finding the distance using the prop which flew 2 hrs longer
2.857 * 150 = 428.6 mi also, confirms our solution

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The headstart for the prop plane is:

mi
---------------------
Start a stop watch when the jet plane leaves
Let = the distance in miles the jet travels
until it catches up with the prop plane
Let = the time on the stop watch in hours
when the jet catches up with the prop plane
-------------------------------------
Equation for prop plane:
(1)
Equation for the jet:
(2)
----------------------
Substitute (2) into (1)
(1)
(1)
(1)
-----------------
(2)
(2)
They are 428.57 mi from starting point
when jet catches prop plane
--------------
check:
(1)
(1)
(1)
(1)
(1)
OK