1. When I see a : b, I know this means a/b = a to b.[/1QUOTE]
NO! It means that if you were to divide the totality into a+ b equal parts, a of them would be one thing and b of them the other.
"The ratio of the number of miles Nash ran to the number of miles he walked improved 8:5" means that out of every 8+ 5= 13 miles he ran 8 miles and walked 5 miles. Of course to find the actual number of miles we would need to know the total number of miles walked and run. MathLover1 somehow discovered that the total was to be 26 miles. 26/13= 2 so dividing 26 into 13 parts, each part is 2 miles. He ran 8(2)= 16 miles and walked 5(2)= 10 miles. Of course 16+ 10= 26.
2. I didn't pay close attention to the words ran and walked.
3. When I see the word mile or miles in applications, I assume that somewhere along the way, I will need to use the fact that one mile is the same as 5,280 feet.
You might want to get over that! Try THINKING about what the problem says, instead.
4. Why did you add the ratios?
5. Where did you get 26 miles?
6. What information in the problem said to calculate
(ran)/(total ratios) times 26?
26 miles is the length of one marathon. Of course, you don't necessarily one marathon's length each week to train for a marathon! This was your problem. What did IT say?
Do you understand why I struggle with word problems? By the way, this is a middle school application. It's funny to know that a person reviewing precalculus struggles with grades 6 through 12 applications. Ha!
Weak English? Poor reasoning skills? In word problems, you are not told what to do. You have to decide that yourself. Like making a "battle plan".