SOLUTION: A military plane carrying heavy cargo can fly at an average rate of 400 mph. Another plane carrying soldiers can fly at an average rate of 600 mph. Both planes leave the same airba

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Question 540553: A military plane carrying heavy cargo can fly at an average rate of 400 mph. Another plane carrying soldiers can fly at an average rate of 600 mph. Both planes leave the same airbase at the same time and are headed to the same destination. If the cargo plane took two and a half hours longer to arrive at the destination than the plane carrying soldiers, then how far is the destination?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A military plane carrying heavy cargo can fly at an average rate of 400 mph.
Another plane carrying soldiers can fly at an average rate of 600 mph.
Both planes leave the same airbase at the same time and are headed to the same destination.
If the cargo plane took two and a half hours longer to arrive at the destination than the plane carrying soldiers, then how far is the destination?
:
Let t = travel time of the 600 mph plane
then
(t+2.5) = travel time of the 400 mph
:
Write a distance equation: dist = speed * time
Both planes travel the same distance
:
600t = 400(t+2.5)
600t = 400t + 1000
600t - 400t = 1000
200t = 1000
t = 1000/200
t = 5 hrs for the fast plane
:
Find the distance
600*5 = 3000 mi
:
Check the distance using the slower plane which traveled for 7.5 hr
400*7.5 = 3000 mi, confirms our distance