SOLUTION: Joseph traveled from Boston to Birmingham at 50 mph and then back to Boston at 40 mph. What was Joseph's average speed on the round trip?

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Question 1197136: Joseph traveled from Boston to Birmingham at 50 mph and then back to Boston at 40 mph. What was Joseph's average speed on the round trip?
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39628)   (Show Source): You can put this solution on YOUR website!
B to B          50       d/50           d
B to B          40       d/40           d
TOTAL                   d(1/50+1/40)   2d





Simplify and compute.
Answer by greenestamps(13206)   (Show Source): You can put this solution on YOUR website!


The distances there and back are the same, and the ratio of the speeds is 50:40 = 5:4. That means the ratio of times spent at the two speeds was 4:5.

So he spent 4x hours going, at 50mph, traveling 4x(50) = 200x miles; and he spent 5x hours returning, at 40mph, traveling 5x(40) = 200x miles.

The round trip was then 400x miles in 9x hours, making his average speed 400/9 = 44 4/9 mph.

ANSWER: 44 4/9 mph

Or you can work the problem as a weighted average: he spent 4/9 of his time at 50mph and 5/9 of his time at 40mph:

(4/9)(50)+(5/9)(40) = 200/9+200/9 = 400/9 = 44 4/9
Answer by ikleyn(52866)   (Show Source): You can put this solution on YOUR website!
.
Joseph traveled from Boston to Birmingham at 50 mph and then back to Boston at 40 mph.
What was Joseph's average speed on the round trip?
~~~~~~~~~~~~~~~ 

For the average speed of the round trip (when the distances of both parts of the trip 
are the same) use the formula


    average speed =  =  =  = 44.444 mph  (rounded).    ANSWER

Solved.

----------------

For this formula see the lesson
    - Calculating an average speed: a train going from A to B and back
in this site.   Find there many other similar solved problems.



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