SOLUTION: How far from an airport can an airplane fly and return in 8 hours, if its outgoing speed is 160 kilometers per hour and its returning speed is 240 kilometers per hour?
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Question 735210: How far from an airport can an airplane fly and return in 8 hours, if its outgoing speed is 160 kilometers per hour and its returning speed is 240 kilometers per hour? Found 4 solutions by lynnlo, ikleyn, greenestamps, josgarithmetic:Answer by lynnlo(4176) (Show Source):
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How far from an airport can an airplane fly and return in 8 hours, if its outgoing speed is 160 kilometers per hour
and its returning speed is 240 kilometers per hour?
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Let's 'd' be this unknown distance to fly from the airport, in kilometers.
Then the time to fly out is hours;
the time to return back is hours,
and the sum of these two pieces of time is 8 hours
+ = 8.
It is your equation to find 'd'.
To find it, multiply all the terms by the least common denominator, which is 480.
You will get
3d + 2d = 8*480,
5d = 3840,
d = 3840/5 = 768 kilometers.
ANSWER. The distance to fly from the airport is 768 kilometers.
Here is a very different solution method than the one shown by the other tutor.
The ratio of the two speeds is 160:240 = 2:3; since the distances out and back are the same, the ratio of the times at the two speeds is 3:2. That means 3/5 of the time is at the lower speed and 2/5 is at the higher speed.
The total time is 8 hours; 3/5 of that total time is 24/5 hours, or 4 4/5 hours.
Flying at 160 km/h for 4 4/5 hours, the plane can fly (160)(24/5) = 32*24 = 768 km.
To check that answer, we can find that the distance the plane flies at 240 km/h for 16/5 hours is (240)(16/5) = 48*16 = 768 km.
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