SOLUTION: An airplane has enough fuel for a 5 hour flight. It goes 225 mile per hour with the wind on the way out and on the return trip goes 180 mph. How far can the plane fly?

Question 1059270: An airplane has enough fuel for a 5 hour flight. It goes 225 mile per hour with the wind on the way out and on the return trip goes 180 mph. How far can the plane fly?
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!
An airplane has enough fuel for a 5 hour flight.
It goes 225 mile per hour with the wind on the way out and on the return trip goes 180 mph.
How far can the plane fly?
:
let d = the one way distance to the point of no return
:
Write a time equation, time = dist/speed
time out + time back = 5 hrs
+ = 5
Find the least common multiple of 225 & 180, by prime factoring
225: 3*3*5*5
180: 2*2*3*3*5
LCM: 2*2*3*3*5*5 = 900
Multiply equation by 900
900* + 900* = 900*5
Cancel the denominators
4d + 5d = 4500
9d = 4500
d = 4500/9
d = 500 mi to the point of no return
;
:
See if this checks out by finding the actual time each way
500/225 = 2.22 hrs
500/180 = 2.78 hrs
----------------------
total time: 5 hrs

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the one-way distance of the trip in miles
Let = the plane's time in hrs
--------------------------------
Equation for flying with the wind
(1)
Equation for flying against the wind
(2)
---------------------------------
By substitution:

hrs
---------------------------
(1)
(1)

The plane can fly 1000 miles
--------------------------------
check:
(2)
(2)
(2)
(2)
(2)
OK

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