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?

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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) About Me  (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
d%2F225 + d%2F180 = 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*d%2F225 + 900*d%2F180 = 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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the one-way distance of the trip in miles
Let +t+ = the plane's time in hrs
--------------------------------
Equation for flying with the wind
(1) +d+=+225t+
Equation for flying against the wind
(2) +d+=+180%2A%28+5+-+t+%29+
---------------------------------
By substitution:
+225t+=+180%2A%28+5+-+t+%29+
+225t+=+900+-+180t+
+405t+=+900+
+t+=+20%2F9+ hrs
---------------------------
(1) +d+=+225%2A%28+20%2F9%29+
(1) +d+=+500+
+2d+=+1000+
The plane can fly 1000 miles
--------------------------------
check:
(2) +d+=+180%2A%28+5+-+t+%29+
(2) +d+=+180%2A%28+5+-+20%2F9+%29+
(2) +d+=+180%2A%28+45%2F9+-+20%2F9+%29+
(2) +d+=+180%2A%28+25%2F9+%29+
(2) +d+=+500+
OK