SOLUTION: Solve the following word problems: A: Tina can run 12 miles in the same time it takes her ti bicycle 72 miles. If her bicycling rate is 20 miles/hour faster than her running rat

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Question 147020: Solve the following word problems:
A: Tina can run 12 miles in the same time it takes her ti bicycle 72 miles. If her bicycling rate is 20 miles/hour faster than her running rate, find each rate.
B: Kevin earned $165 interest for 1 year on investment of $1500. At the same rate, what amount of interest would be earned by an investment of $2500?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A: Tina can run 12 miles in the same time it takes her to bicycle 72 miles. If her bicycling rate is 20 miles/hour faster than her running rate, find each rate.
:
Let s = T's running speed
then
(s+20) = T's biking speed
:
Write a time equation: Time =
Time to Bike 72 mi = Time to run 12 mi
=
Cross multiply, find s:
:
72s = 12(s+20)
:
72s = 12s + 240
:
72s - 12x = 240
s =
s = 4 mph is T's running speed
and
24 mph is T's biking speed
;
:
Check solutions to see if the times are equal
72/24 = 3 hrs
12/4 = 3 hrs
:
;
B: Kevin earned $165 interest for 1 year on investment of $1500. At the same rate, what amount of interest would be earned by an investment of $2500?
:
Using the interest formula PRT = I; here t = 1 so it is just:
1500R = 165
R =
R = .11 or 11% interest
:
For $2500 at 11%
.11 * 2500 = $275
:
You can also use ratio: (x = interest amt on $2500))
=
1500x = 165 * 2500
x =
x = $275