SOLUTION: An airplane travels west at 180 km/h, and returns east with the jet stream at 300 km/h. What was the average speed in km/h for the whole trip?

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Question 1150797: An airplane travels west at 180 km/h, and returns east with the jet stream at 300 km/h. What was the average speed in km/h for the whole trip?
Found 3 solutions by ikleyn, Alan3354, greenestamps:
Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.

I will assume that both rates of 180 km/h  and  300 km/h are the  ground-speeds.


Let " d " be one way distance.


Then the total time is  d%2F180 + d%2F300  hours.    (1)


Then the average rate is the total distance (2d kilometers, in this case), divided by the total time (1)


    average rate = %282d%29%2F%28d%2F180%2Bd%2F300%29 = 2%2F%281%2F180+%2B+1%2F300%29 = 2%2F%28%28300%2B180%29%2F%28300%2A180%29%29 = 2%2F%28%28480%2F%28300%2A180%29%29%29 = %282%2A300%2A180%29%2F480 = 225 km/h.     ANSWER

Solved.


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
An airplane travels west at 180 km/h, and returns east with the jet stream at 300 km/h. What was the average speed in km/h for the whole trip?
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Avg = 2*180*300/(180+300)
Avg = 225 km/hr
===================
Airplanes (and boats) don't use km/hr.
They use knots.
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The speed of the jet stream given is only ~ 30 knots.
Jet stream speeds are typically 100 knots or greater.
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Three (3) different ways are shown to solve the problem.
The average speed of a round-trip, or a trip of 2 legs of equal length can be solved by the method I used.
It's similar to parallel work, parallel resistors, etc., with the only difference the factor of 2.
I'm not a proponent of memorizing formulas (tho some are necessary), but I think the one I used is worth remembering (for math problems).
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Look at the Michelson-Morley experiment on Google or Wikipedia.
They disproved the existence of "phlogiston." (JK)

Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


The ratio of the speeds is 180:300 = 3:5.

Since the distances are the same, the ratio of the times is 5:3.

So the plane flies at 180km/h for 5/8 of the time and at 300km/h for 3/8 of the time. The average speed in km/h is then

%285%2F8%29%28180%29%2B%283%2F8%29%28300%29+=+%28900%2F8%29%2B%28900%2F8%29+=+1800%2F8+=+225