SOLUTION: During rush hour, Fernando can drive 35 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Fernando's rate on the side roads is 9 mi/h

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Question 72846: During rush hour, Fernando can drive 35 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Fernando's rate on the side roads is 9 mi/h faster than his rate on the freeway, find his rate on the side roads.
I came up with 65 and was wanting to check to see if this is right. Thanks.
Found 2 solutions by ankor@dixie-net.com, bucky:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Fernando can drive 35 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Fernando's rate on the side roads is 9 mi/h faster than his rate on the freeway, find his rate on the side roads.
:
Let s = his speed on the side roads
:
Then (s-9) = his speed on the freeway
:
Since the times are equal, write a time equation; time = dist/speed:
:
Sideroad time = freeway time
=
:
Cross multiply and you have:
35(s-9) = 30s
35s - 315 = 30s
35s - 30s = + 315
5s = 315
s = 63 mph on the side-road, you were close
:
:
Check to see if the times are, in fact equal. Freeway speed: 63-9 = 54 mph
30/54 = .556
35/63 = .556

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Close to being right.
.
Let's use the equation D = R*T ... Distance = Rate * Time ... for both the freeway and side
road trips.
.
We are told that the time is the same for both of these trips. But if the speed on the
freeway is called S, then the rate on the side roads is S+9.
.
The distance on the side road is 35 miles, and, as we stated above, the rate is S+9.
So for the side road trip the distance equation becomes:
.

.
Similarly, for the freeway trip the distance is 30 miles and the rate is S. So for this route
the distance equation is:
.

.
Solve both of these equations for T. The side road equation becomes:
.

.
and the freeway equation becomes:
.

.
Because the time is the same in both cases, the right sides of these equations must be
equal. So we can write:
.

.
A short way of solving this is to multiply along both diagonals and set the two products
equal. In other words, multiply the numerator of one fraction by the denominator
of the other and do the same for the other numerator and denominator pair. In this case
multiply the 35 time S and then multiply the 30 times (S+9). Then set the products
equal to get:
.

.
do the distributive multiplying on the right side to get:
.

.
then subtract from both sides and the equation is reduced to:
.

.
Divide both sides by 5 and you get . But this is the freeway speed and you
were asked to find the speed on the side road which is 9 mph faster. So add 9 to 54 and
you get that the side road speed is 63 mph.
.
Hope this helps you to find the source of the difference in our answers. You seem to
have been pretty close so it's probably a minor mistake by one of us.
.