Brooke
I am going to answer this because nobody else has yet but I believe there must be a simpler way to get the answer although this does get you to the answer.
The classic formula is D = R * T and you need to have this formula two times, one for each way.
On the way there you know only distance is 46 so it is 46 = R * T
On the way back you know you the distance is the same, 46 but the rate is 23 miles less and the time is 1 hour less so the formula is 46 = (R-23)(T-1).
Now that you have these 2 formulas you can do some calculations, these are what I did.
On the second I multiplied it out with FOIL:
46 = RT + R -23T -23
You know that RT =46 so you can do that first substitution
46 = 46 + R -23T -23
You can then subtract 46 from both sides and that leave = = R - 23T - 23 which still leaves you with 2 variables and you need one. Going back to the equation 46 = RT I solved for R = 46/T and substituted the R with this
46/T -23T - 23 = 0
You can then multiply each term by T to give you a standard polynomial
46 - 23T^2 - 23T = 0
Divide out the 23 and -1 for the simpler version
T^2 + T - 2 = 0 and factor this to (T-1)(T+2) and you know only T-1 is a possible answer as your time can't be a negative number so T = 1 hour.
Go back to the 2nd equation and solve for R
46 = (R-23)(1+1)
46 = 2R-46
92 = 2R
R = 46
So the original trip was 1 hour at 46 miles per hour and went 46 miles
Returning was 2 hours at 23 miles per hour and went 46 miles
In this case it was probably just easier to guess but it is important to know how to use the 2 formula method as that is the usual way to handle these
All the best
Lori
