SOLUTION: Rosie ran to the park at 7 miles per hour and walked back home at 3 miles per hour. How many miles was it to the park if the round trip took 20 hours? Begin by drawing a diagram of

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Question 1202341: Rosie ran to the park at 7 miles per hour and walked back home at 3 miles per hour. How many miles was it to the park if the round trip took 20 hours? Begin by drawing a diagram of distances traveled and writing the distance equation on your paper.
Found 3 solutions by math_tutor2020, josgarithmetic, Alan3354:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: 42 miles

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Explanation:

x = distance, in miles, from Rosie's house to the park.

Draw a rough sketch of what's going on.


Here's a table to organize the knowns and unknowns so far.
Distance (miles)Rate (mph)Time (hrs)
Runningx7x/7
Walkingx3x/3

Relevant formulas:
Distance = rate*time
time = distance/rate

The two time values x/7 and x/3 must add to the grand total of 20 hours. This is the round trip time.

time1+time2 = round trip time
x/7 + x/3 = 20
21*(x/7 + x/3) = 21*20
21*(x/7) + 21*(x/3) = 420
3x + 7x = 420
10x = 420
x = 420/10
x = 42

The distance from her home to the park is 42 miles

She runs at 7 mph, so she took x/7 = 42/7 = 6 hours to run to the park.
Rosie walks at 3 mph. She took x/3 = 42/3 = 14 hours to walk back home.
That's a total of 6+14 = 20 hours to verify we have the correct answer.

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Follows an often used form.
Here unknown variable, x for unknown time to run. 
              SPEED          TIME        DISTANCE

RAN TO            r             x          d

WALKED BACK       w            t-x        d

TOTAL                           t        2d

rx=w%28t-x%29
rx=wt-wx
rx%2Bwx=wt
highlight_green%28x=%28wt%29%2F%28r%2Bw%29%29


You are given r=7, w=3, and t=20.
Evaluate x.
Then d=rx.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Rosie ran to the park at 7 miles per hour and walked back home at 3 miles per hour. How many miles was it to the park if the round trip took 20 hours? Begin by drawing a diagram of distances traveled and writing the distance equation on your paper.
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Avg speed of a round trip = 2v%5B1%5D%2Av%5B2%5D%2F%28v%5B1%5D%2Bv%5B2%5D%29
= 2*7*3/(7+3) = 4.2 mi/hr
d = r*t = 84 mi
---> 42 miles each way