SOLUTION: I am faced with what I believe to be an open-ended assessment question related to proportions and ratios. The question is as follows: Tony and Ivia started walking south from th

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Question 142535: I am faced with what I believe to be an open-ended assessment question related to proportions and ratios. The question is as follows:
Tony and Ivia started walking south from the same location at the same time. Ivia walked 8 miles and walked 1 mile per hour faster than Tony who walked 6 miles. They each walked for the same amount of time.

a. I need to describe how a proportion could be used to find the rate that each person walked at.

b. The next day they both walked 6 miles, and Ivia again walked 1 mile per hour faster than Tony, who walked 3 miles per hour. Determine whether a proportion could be used to find how long each person walked
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Tony and Ivia started walking south from the same location at the same time. Ivia walked 8 miles and walked 1 mile per hour faster than Tony who walked 6 miles. They each walked for the same amount of time.
:
a. I need to describe how a proportion could be used to find the rate that each person walked at.
:
Let s = T's walking speed
Then (s+1) = I's speed
Using proportion:
=
Cross multiply
8s = 6(s+1)
8s = 6s + 6
8s - 6s = 6
2s = 6
s =
s = 3 mph is T's speed; Then 4 mph is I's speed
:
Check solutions by finding the time of each; time = dist/speed
8/4 = 2 hrs
6/3 = 2 hrs
:
:
b. The next day they both walked 6 miles, and Ivia again walked 1 mile per hour faster than Tony, who walked 3 miles per hour. Determine whether a proportion could be used to find how long each person walked.
:
From the information we know T's speed is 3 mph and I's speed is 4 mph
Time = dist/speed, so we know time varies inversely to the speed
:
ratio would then be:
=