SOLUTION: James walked 4 mph for a certain amount of time and 3 mph for a certain amount of time. He went 27 miles. Had he walked 3 mph faster throughout, he would have walked 51 miles.

If you need immediate math help from PAID TUTORS right now, click here. (paid link)
Click here to see ALL problems on Travel Word Problems

Question 274474: James walked 4 mph for a certain amount of time and 3 mph for a certain amount of time. He went 27 miles.
Had he walked 3 mph faster throughout, he would have walked 51 miles. How long did he walk for 4 mph?
I feel like there is a variable missing, but my instructor says that there is not. I have tried this question 47 times. I don't have the answer to check if what I have is correct, but none of my work checks out.
I use
4(x) + 3(y) = 27
3(x-y)=51
My answer is 9 hours at 3 mph, and 6.75 at 4mph. If this is true, then why did they bother to give me the second part of the question. It wasn't even used.
Any help that can be offered is appreciated.

Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
let x="4 mph time" and y="3 mph time"

4x + 3y = 27 ___ 8x + 6y = 54

(4 + 3)x + (3 + 3)y = 51 ___ 7x + 6y = 51

subtracting equations ___ x = 3

substituting ___ 4(3) + 3y = 27 ___ y = 5