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Rate problem from official guide

by aalradadi » Sun Dec 01, 2013 12:00 pm

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"After driving to a riverfront parking lot, Bob plans to run south along the river, turn around, and return to the parking lot, running north along the same path. After running 3.25 miles south, he decides to run for only 50 minutes more. If Bob runs at a constant rate of 8 minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes?

(A) 1.5
(B) 2.25
(C) 3.0
(D) 3.25
(E) 4.75"

Excerpt From: Graduate Management Admission Council (GMAC). "The Official Guide for GMAT Review." iBooks.
This material may be protected by copyright.

Check out this book on the iBooks Store: https://itunes.apple.com/WebObjects/MZS ... =519401729


Can someone explain this problem better than the way the OG did?
Thanks.
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by GMATGuruNY » Sun Dec 01, 2013 12:39 pm
aalradadi wrote:"After driving to a riverfront parking lot, Bob plans to run south along the river, turn around, and return to the parking lot, running north along the same path. After running 3.25 miles south, he decides to run for only 50 minutes more. If Bob runs at a constant rate of 8 minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes?

(A) 1.5
(B) 2.25
(C) 3.0
(D) 3.25
(E) 4.75
Convert the rate to MILES PER MINUTE:
1 mile per 8 minutes = 1/8 mile per minute.

Initial distance traveled south = 3.25 = 13/4 miles.
At a rate of 1/8 mile per minute, the time to travel 13/4 miles south = d/r = (13/4)/(1/8) = (13/4)(8) = 26 minutes.

Since Bob plans to run for 50 more minutes, the total time to run south and north = 26+50 = 76 minutes.
Thus, the total time run south = 76/2 = 38 minutes.

Since Bob has already run for 26 minutes, he runs south an additional 12 minutes.
Additional distance traveled in 12 minutes = r*t = (1/8) * 12 = 1.5 miles.

The correct answer is A.
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by aalradadi » Mon Dec 02, 2013 8:43 am
Thanks Mitch, your the best!!
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by Mathsbuddy » Mon Dec 02, 2013 8:59 am
Speed = 1/8 miles per minute

Distance = Speed * Time = 1/8 * 50 = 6.25 miles


Bob's route (using positive for North, negative for South):
-n miles +n miles -3.25 miles then mixed direction 6.25 miles split to allow return:

6.25 - 3.25 = 3 miles surplus

3 miles split in two = 1.5 miles

So Bob's route is: -n +n -3.25 -1.5 + 1.5 + 3.25 miles = 0 displacement.

So ANSWER = (A) 1.5
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by Balla » Fri Jul 28, 2017 7:38 pm
I see comversions to 1/8 mile per minute but that isn't necessary.

He has gone 3.25 miles.


Then he goes for 50 mins at a rate of 8 mins per mile. So (8/1)=(50/x)

X=50/8 or 6.25

So total distance is 3.25 +6.25=9.5
Half of that is 4.75. He already went 3.25 miles.

He can go 4.75-3.25 more miles south.
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by Matt@VeritasPrep » Sun Aug 06, 2017 11:15 pm
aalradadi wrote: Excerpt From: Graduate Management Admission Council (GMAC). "The Official Guide for GMAT Review." iBooks.
This material may be protected by copyright.
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by Matt@VeritasPrep » Sun Aug 06, 2017 11:18 pm
Let me be useful and add an explanation too!

Bob will run x more miles south, then turn around, run those x miles again north, then run the final 3.25 miles north. That means that

Total distance to run = x + x + 3.25
Total time = 50 minutes = 5/6 of an hour

We know Distance = Rate * Time, so

(2x + 3.25) = Rate * (5/6)

Bob runs a mile in 8 minutes, so he runs (60/8) miles per hour. Plugging that in for his rate, we get

(2x + 13/4) = (60/8) * (5/6)

(2x + 13/4) = 50/8

2x = 3

x = 1.5
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by Matt@VeritasPrep » Sun Aug 06, 2017 11:21 pm
Another approach:

Bob is going to run for 50 minutes at (60/8) miles per hour, so he'll be able to run (5/6) * (60/8) => 25/4 miles.

Adding in the distance Bob has ALREADY run (3.25 miles), he'll run a total of 38/4 miles in all.

Half of that, or 19/4, will be south. He's already run 13/4 miles south, so he has 6/4 left, or 1.5.
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by ceilidh.erickson » Mon Aug 07, 2017 8:54 am
Matt@VeritasPrep wrote:
aalradadi wrote: Excerpt From: Graduate Management Admission Council (GMAC). "The Official Guide for GMAT Review." iBooks.
This material may be protected by copyright.
Somewhere on the interwebs, Ceilidh is smiling! :D
Haha I don't know how I've established myself as the only stickler for the rules!

Anyway, here's another approach. (Or not really a *different* approach, but a visual one).

Distance problems are often great candidates for drawing a picture. Here's Bob running the initial 3.25 miles:

Image

Now he needs to run some unknown number of miles further:

Image

Then he'll turn around and run the whole way back:

Image

This helps us to see that he'll be running that X distance twice, plus the original 3.25 back.

We can use quick mental estimation to eliminate answer choices:
~3 miles x 8 min per mile = > 24 min
So that's about half of the 50 total min he wants to spend.
The remaining ~half should be split between X miles south & X miles back north.
Therefore, anything 3 or greater is clearly too much. We can eliminate C, D, and E.

B should also feel too large, but we can double-check: if X = 2.25, then 2X would be 4.5 miles. Multiply that by 8min/mi --> 36 mi. That's clearly too much time, since we know that the 3.25 mi accounts for more than 24 min.

Therefore, the answer must be A.
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Harvard Graduate School of Education
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by Jeff@TargetTestPrep » Wed Aug 09, 2017 12:38 pm
aalradadi wrote:"After driving to a riverfront parking lot, Bob plans to run south along the river, turn around, and return to the parking lot, running north along the same path. After running 3.25 miles south, he decides to run for only 50 minutes more. If Bob runs at a constant rate of 8 minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes?

(A) 1.5
(B) 2.25
(C) 3.0
(D) 3.25
(E) 4.75"
We are given that Bob plans to run south along the river, turn around, and return to where he started.

We know that his run south (from the parking lot) and his run north (back to the parking lot) are equal in distance. We will use this information later in the solution.

We are also given that Bob's rate is 8 minutes per mile, or, in other words, (since Rate = Distance/Time) his rate is 1 mile per 8 minutes or 1/8.

We are told that Bob has already run 3.25 miles south, and he wants to run for 50 minutes more. Thus, we calculate how far Bob will go in the remaining 50 minutes.

Distance = Rate x Time

Distance = 1/8 x 50

Distance = 50/8 = 25/4 = 6.25 miles

Thus, we know that Bob's total running distance will be 6.25 + 3.25 = 9.5 miles. Because we know the distance is the same both ways, we know that each leg of his trip is 9.5/2 = 4.75 miles. Since Bob has ALREADY RUN 3.25 miles south, he can run 4.75 - 3.25 = 1.5 miles more. At that point, he will have to turn around and head back north to the parking lot.

Answer: A

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by Matt@VeritasPrep » Fri Aug 18, 2017 1:54 pm
ceilidh.erickson wrote: Haha I don't know how I've established myself as the only stickler for the rules!
... because you've outstickled the stickliest of us on the forum, time and again! :)

I hope I'm still the most indignant about ² over ^2, though. I can't see how in 2017 any expert imagines him/herself halfway credible if he/she won't bother or can't learn how to type that.
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