SOLUTION: I need help on solving this word problem: Trisha ran to the park and then walked home. It took her 1/2 hours to get to the park and 1 hour adn 20 minutes to get home. If she r

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Question 6597: I need help on solving this word problem:
Trisha ran to the park and then walked home. It took her 1/2 hours to get to the park and 1 hour adn 20 minutes to get home. If she runs 5 miles an hour faster then she walks, how far does she live from the park?
Answer by prince_abubu(198) (Show Source):
You can put this solution on YOUR website!
We'll work with the equation r * t = d. In this situation, we have two different rates and two different times but the same distance. Let's label some variables:

= walking speed
= running speed, which really is
= time it took her to run to the park, which is 1/2 hour
= time it took her to walk, which is 1 1/3 hours (that's 1 hour and 20 minutes in fraction form)

Since she will walk and run the same distance, we can say

<---- We are actually interested in finding the distance, but in this case, we have to find the rates first.

<----- We did some substitutions and turned 1 1/3 to an improper fraction.

<---- multiply both sides by 3 to get rid of the fraction.

<---- multiply both sides by 2 to get rid of the other fraction

<---- expand using distributive property for the right side

<----- Her walking speed was 3 miles per hour. Since it took her 1 hour and 20 minutes (4/3 of an hour) to walk at 3 miles per hour, the distance would've been r*t = (3)*(4/3) = 4 miles.