SOLUTION: Please help! I am at a total loss on this one. At noon Joyce drove to the lake at 30 miles per hour, but she made the long walk back home at 4 miles per hour. How long did she w

Question 37083This question is from textbook Alegra I
: Please help! I am at a total loss on this one.
At noon Joyce drove to the lake at 30 miles per hour, but she made the long walk back home at 4 miles per hour. How long did she walk if she was gone for 17 hours? How far did she walk? Begin by drawing a diagram fo distances traveled and writing the distance equation. This question is from textbook Alegra I

Answer by jcmtnez(53) (Show Source): You can put this solution on YOUR website!
You know that d=v*t, where d is the distance and v is the speed and t is the time, the proble give you two speeds and the total time.
Lets call t1 the time that it take her to go from his house to the lake, and lets call t2 the time that it take her to go from the lake to his house. The distance from his house to the lake is constant, I mean that the distance does not change. Now lets call v1 the speed of 30mph and v2 the speed of 4mph. The time t is equalt to t=d/v distance divede by speed. Now I hope that you understand the following equation:
d/v1+d/v2=t The sum of the time that take her to go to the lake from his house and the time that take her to go from the lake to his house it is the total time. Now we only have to use the given data.
v1=30mph
v2=4mph
t=17hours
d/30+d/4=17 Now we only have to solve this equation to know the total distance that she travelled.

2d+15d=1020
17d=1020
d=60 miles she travelled, and therefore the distance from his house to the lake is 30 miles.
If you have any doubt ask me.

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