Sam took traveled 8 hrs to his sisters house. The return trip took 7 hrs because the speed was 3 mi/hr faster. What was the Sam's speed each way?

I like to set up a chart for these kind of problems, they become very easy that way

D=r*t , Distance = rate*time

--------D------R-------T
.............................
trip #1 8x-----x------8
trip #2 7(x+3) x+3----7

the two distances are the same
----> 8x = 7(x+3)

etc

I knew the distance would be the same what I am having a problem with finding the the speed each way.

To find the speed for each trip, you can use the formula D = R * T, where D is the distance, R is the rate or speed, and T is the time taken.

For the first trip, the distance is the same as the distance for the return trip, so we can set up an equation using this information. Let's call the speed for the first trip "x" (in miles per hour). The time for the first trip is 8 hours.

Therefore, for the first trip, D = R * T becomes D = x * 8.

For the return trip, the speed is 3 miles per hour faster than the speed for the first trip. So, the speed for the return trip would be x + 3 (in miles per hour). The time for the return trip is 7 hours.

Therefore, for the return trip, D = R * T becomes D = (x + 3) * 7.

Since the distance for both trips is the same, we can set up an equation:

8x = 7(x + 3).

Now, we can solve for x by simplifying and then solving the equation:

8x = 7x + 21.

Subtracting 7x from both sides:

x = 21.

So, Sam's speed for the first trip is 21 miles per hour, and his speed for the return trip is x + 3 = 21 + 3 = 24 miles per hour.