SOLUTION: A car drove from town A to town B at an average of 60 mph. On the return trip from town B to town A the car took exactly the same route. It was foggy and the car only averaged 40 m

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Question 1078220: A car drove from town A to town B at an average of 60 mph. On the return trip from town B to town A the car took exactly the same route. It was foggy and the car only averaged 40 mph on the return trip. What is the average speed over the entire trip?
Found 3 solutions by Fombitz, ikleyn, solver91311:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate * Time = Distance
60%2At%5B1%5D=D
t%5B1%5D=D%2F60
and
40%2At%5B2%5D=D
t%5B2%5D=D%2F40
So then the total distance traveled was 2D and the total time used was t%5B1%5D%2Bt%5B2%5D so the average rate is,
R%5BAVE%5D=%282D%29%2F%28t%5B1%5D%2Bt%5B2%5D%29
Substituting,
R%5BAVE%5D=%282D%29%2F%28D%2F60%2BD%2F40%29
.
.
R%5BAVE%5D=2%2F%281%2F60%2B1%2F40%29
.
.
R%5BAVE%5D=2%2F%282%2F120%2B3%2F120%29
.
.
R%5BAVE%5D=2%2F%285%2F120%29
.
.
R%5BAVE%5D=240%2F5
.
.
Work that out for your final answer.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let D be the distance between the cities.

Then the time for the trip from A to B is D%2F60 hours.

     The time for the trip from B to A is D%2F40 hours.


The total time for the round trip is D%2F60+%2B+D%2F40 = %2840D+%2B+60D%29%2F%2860%2A40%29 = %28100%2AD%29%2F%2860%2A40%29 hours.


The length of the round trip is 2D.


Hence, the average speed is %282D%29%2F%28%28100%2AD%29%2F%2860%2A40%29%29 = %282%2A60%2A40%29%2F%28100%29 = 48 mph.

Solved.

For the solution of similar problem with detailed explanations see the lesson
    - Calculating an average speed: a train going from A to B and back
in this site.



Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Begin with , distance equals rate times time

As for the initial trip, we do not know the distance and we do not know the time taken. So all we know is that , or more conveniently, .

As for the return trip, we have a similar relationship, namely . But since , we know that the return trip must have taken times as long as the initial trip. Hence, .

The average speed is then the total distance, , divided by the total time, , which is to say:



However, we know from the relation describing the initial trip that , so



You can do your own arithmetic.

John

My calculator said it, I believe it, that settles it