rational expression word problem

lmsseattle

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I think this problem belongs on this thread. A few of us in my class are having difficulty with this problem:

Trisha ran to the park and then walked home. It took her 1/2 hour to get to the park and 1 hour and 20 minutes to get home. If she runs 5 miles an hour faster than she walks, how far does she live from the park?

I keep coming up with two variables when I create my equation. Here's what I have:

d = round trip from home to park
d/2 = distance from her home to park (answer)

rate walking = r
rate running = r+5

time = 80 minutes walking
time = 30 minutes running

Equation:

d = 80r + 30(r+5)

Now I'm stuck with two variables and can't figure out how to continue. Thanks for your help.
 
I think this problem belongs on this thread. A few of us in my class are having difficulty with this problem:

Trisha ran to the park and then walked home. It took her 1/2 hour to get to the park and 1 hour and 20 minutes to get home. If she runs 5 miles an hour faster than she walks, how far does she live from the park?

I keep coming up with two variables when I create my equation. Here's what I have:

d = round trip from home to park
d/2 = distance from her home to park (answer)

rate walking = r
rate running = r+5

time = 80 minutes walking
time = 30 minutes running

Equation:

d = 80r + 30(r+5)

Now I'm stuck with two variables and can't figure out how to continue. Thanks for your help.

I assume Trisha ran to the park from home and walked back to home from the park.

Assume

the distance frome park to home = d

speed of walking = W

speed of running = W+5

then

½ = d/(W+5) → 2d = W+5 → W = 2d - 5
and

4/3 = d/W → W = ¾ * d

then

2d - 5 = ¾ * d

One equation - one unknown → solve it!!
 
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thank you - very helpful.

But I am uncertain about how you thought about the problem. You essentially came up with a W=W equation...

W = 2d - 5
and
W = ¾ * d

then
2d - 5 = ¾ * d

and I don't understand how you came to see the problem in this way. Can you give some explanation how you approached the problem? The greatest difficulty I am having with these rational expression word problems is how to approach the problem when different information is given, especially when it isn't immediately a straight forward d=tr or t=d/r or r=d/t type of equation.
 
how far does she live from the park?

d = round trip from home to park

d = 80r + 30(r+5)

I think that you may have confused yourself in two ways.

Firstly, you chose to express the given times in minutes without also converting the given 5mph to the equivalent number of miles-per-minute. Rather than making this conversion, it's easier to stick with hours as the time unit.

30 minutes is 1/2 hour, and 80 minutes is 4/3 hours.

Secondly, you wrote an equation for the round-trip distance. The exercise does not ask for the round-trip distance.

If you had instead let d represent the distance between her home and the park, then you could have written two equations.

d = 4/3 r

d = 1/2 (r + 5)

Whenever you have two different expressions representing the same value, those two expressions are equal to one another.

4/3 r = 1/2 (r + 5)

Solve for r, and substitute the result into 4/3 r to find d.

This approach is a straight-forward use of d = rt.
 
All three of these responses have been extremely helpful. Thank you. I will pass this on to my classmates.
 
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