Question 1132034
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Let d be the distance for each leg of the trip.  Then the total time for the trip is<br>
{{{d/180+d/300 = (300d+180d)/(180*300) = ((300+180)d)/(180*300)}}}<br>
The total distance is 2d; the average speed is total distance divided by total time:<br>
{{{2d/(((300+180)d)/(180*300)) = ((2d(180*300))/((300+180)d)) = (2(180*300))/(300+180)}}}<br>
Simplified, that is 225 km/h.<br>
Note the expression could have been simplified along the way; I kept it in this form so you could see where the formula cited by the other tutor came from.<br>
ANSWER: the average speed is 225 km/h.<br>
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Here is a different way I like to use for solving a problem like this.<br>
The ratio of the two speeds is 180:300 = 3:5.  Since the distances are the same, that means the ratio of the times is 5:3.<br>
So for 5/8 of the time the plane is flying at 180 km/h, and for 3/8 of the time it is flying at 300 km/h.  The average speed is then<br>
{{{(5/8)(180)+(3/8)(300) = 900/8 + 900/8 = 900/4 = 225}}}