SOLUTION: Please can somebody help me in this problem: It took a small plane 2 hours to fly 375 miles against the wind than it took the same plane to fly the same distance with the win

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Question 74969: Please can somebody help me in this problem:
It took a small plane 2 hours to fly 375 miles against the
wind than it took the same plane to fly the same distance
with the wind. The rate of the wind was 25 mph. Find the
rate of the plane in caalm air.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It took a small plane 2 hours to fly 375 miles against the
wind than it took the same plane to fly the same distance
with the wind. The rate of the wind was 25 mph. Find the
rate of the plane in calm air.
:
Let s = speed of the plane in calm air
Then:
(s+25) = speed with the wind
and
(s-25) = speed against the wind
:
Write a time equation, Time = distance/speed; (distance given as 375 mi)
:
Time with the wind + 2hr = Time against the wind
375%2F%28%28s%2B25%29%29 + 2 = 375%2F%28%28s-25%29%29
:
Multiply equation by the common denominator, (s+25)(s-25); resulting in:
375(s-25) + 2(s+25)(s-25) = 375(s+25)
:
Multiply what's inside the brackets:
375s - 9375 + 2(s^2 - 625) = 375s + 9375
:
375s - 9375 + 2s^2 - 1250 = 375s + 9375
:
Group like terms on the left:
2s^2 + 375s - 375s - 9375 - 1250 - 9375 = 0
:
2s^2 - 20000 = 0
:
Add 20000 to both sides:
2s^2 = +20000
:
s^2 = 20000/2
:
s^2 = 10000
:
s = sqrt%2810000%29
:
s = 100 mph in calm air
:
:
Check our solution by finding the time at both speeds:
With the wind = 125 mph, and against = 75 mph
375/75 = 5 hrs
375/125= 3 hrs
---------------
Differ = 2 hrs
:
How about this, did it make sense to you? Any questions?