Simple prob - Avg speed

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Hi everyone. I'm taking my very first physics course and can't seem to get a grasp on it. I can solve some problems without problems but get stuck at simple things. I need a little hint on this problem:

A car drives from A to B, half the time at 55 km/h and the other half at 90 km/h. On the way back, the car travels half the distance at 55km/h and the other half at 90km/h. What is the average speed from B to A?

Thanks in advance!
 

HallsofIvy

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Cute problem.

The problem doesn't tell us what the distance between A and B is so let's call it "D" km.
Notice that the problem only asks for the average speed driving back from B to A. All the first part, about how the person got from A to B is irrelevant.

The person drives back from B to A (presumably the same distance D!) going half the distance at 55 mph. If we let T1 be the time at 55 km/h, then 55T1= D/2 so T1= D/110.
He then drives half the distance at 90 km/h. If we let T2 be the time at 90 km/h, we have 90T2= D/2 so T2= D/180.

To find "average speed", we need to divide the distance by the total time so we need to find total time:
The total time is T1+ T2= D/110+ D/180= ((18+ 11)/1980)D= (29/1980)D (180= 18*10 and 110= 11*10 so the least common denominator is 18*11*10= 1980). You could, of course, just use a calculator to get 0.00909+ 0.00555= 0.01465= 29/1980.

The average speed is D/((29/1980)D)= 1980/29= 68.27 km/h.
 

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