How fast did Gail travel on each part of the trip?

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jshaziza

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On a sales trip, Gail drives the 600 miles to Richmond at a certain speed. The return trip is made at a speed that is 10 mph slower. Total time for the round trip was 22 hours. How fast did Gail travel on each part of the trip?

So far all I was able to translate from this problem is r=1200/22 and 600/r-10, where r is the rate. But I know I am missing something so if someone can point it out, I will be able to solve it from there. Thanks for any help.
 
It's 600 miles one way and 1200 miles round trip.

Since d=rt, we can use t=d/r

\(\displaystyle \L\\\frac{600}{r}+\frac{600}{r-10}=22\)

Solve for r.
 
Re: Word problem

jshaziza said:
On a sales trip, Gail drives the 600 miles to Richmond at a certain speed. The return trip is made at a speed that is 10 mph slower. Total time for the round trip was 22 hours. How fast did Gail travel on each part of the trip?

So far all I was able to translate from this problem is r=1200/22

As galactus had shown above - that is not correct

What you found is average speed for the whole trip - that won't help you


and 600/r-10, where r is the rate. But I know I am missing something so if someone can point it out, I will be able to solve it from there. Thanks for any help.
Click to expand...
 
I generally find these problems easier to do/understand if you put them into a table.

..................distance...........rate................time
to................600.................x....................600/x
from............600.................x-10...............600/(x-10)


The distance we can find from the problem because it is 600 miles to Richmond, and the trip is over the same distance both ways.

We are given the information that one direction is 10 mph slower than the other direction. MPH is a rate, thus one of the rates will be our x, and the other will be x-10.

Because we know that distance=rate x time, we can re-arrange this and solve for time (the one variable that we don't know) in terms of distance and rate (the two variables we do know) so Distance/Rate = Time and plug the values for distance and rate into this for your time.

We know from the problem that the round trip took 22 hours, so the time from the to trip added to the time from the return trip is 22. Therefore:

600/x - 600/(x-10) = 22
 
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