"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.
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Can someone explain this problem better than the way the OG did?
Thanks.
Rate problem from official guide
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Convert the rate to MILES PER MINUTE: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
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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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
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
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.
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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Somewhere on the interwebs, Ceilidh is smiling!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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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
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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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.
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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Haha I don't know how I've established myself as the only stickler for the rules!Matt@VeritasPrep wrote:Somewhere on the interwebs, Ceilidh is smiling!aalradadi wrote: Excerpt From: Graduate Management Admission Council (GMAC). "The Official Guide for GMAT Review." iBooks.
This material may be protected by copyright.
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:
Now he needs to run some unknown number of miles further:
Then he'll turn around and run the whole way back:
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.
Ceilidh Erickson
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We are given that Bob plans to run south along the river, turn around, and return to where he started.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 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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... because you've outstickled the stickliest of us on the forum, time and again!ceilidh.erickson wrote: Haha I don't know how I've established myself as the only stickler for the rules!
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.