After driving to a riverfront parking lot, Bob plans to run

Question

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

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ID: 100828

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Official Answer

A

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

ID: 100828

Bunuel · Accepted Answer

Bob runs at a constant rate of  8 minutes per mile , thus in 50 minutes he can cover 50/8=6.25 miles.

Therefore the total round-trip distance Bob covers is 3.25+6.25=9.5 miles.

Half of that distance he runs south, so he runs 9.5/2=4.75 miles south, and since he has already run 3.25 miles, then he can run 4.75-3.25=1.5 miles farther south .

Answer; A.

nave · Answer

rate of  8 min per mile implies to cover  3.25  miles it has taken Bob  3.25*8mins = 26mins

Total time for the entire round trip is  26+50 = 76mins , so half way is covered in  38mins . If Bob has already travelled  26mins  then the remaining time for one way is  12mins .

In  12mins  Bob travels  \frac{12}{8} = 1.5  miles

ScottTargetTestPrep · Answer

Solution: We are given that Bob plans to run south along the river, turn around, and return to where he started. We can draw this out. https://gmatclub.com/forum/download/file.php?id=62021 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 had 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 k6e3QYw.png

shahir16 · Answer

How do we know that he ran half the distance south ? Thanks

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JesseWhelan · Answer

Hi Shair. The question states that Bob will run south along the river and then turn around to return to the parking lot. Since there are only two legs to the journey, namely south and back, this implies that Bob will run half the total distance south.

Hope that helps.
Jesse

raj077 · Answer

Another method :Solve through equations.
Total remaining distance ,Dsouth + Dnorth = 50/8 = 6.25 miles
(1): 3.25 + Dsouth = Dnorth
(2): Dnorth + Dsouth = 6.25

Solve (1) and (2) i.e (1) + (2) => 3.25 + 2*Dsouth = 6.25 => Dsouth = 3/2= 1.5 miles

sayansarkar · Answer

another way to solve this:

Let x be the extra mile that bob can run and make it in 50 mins back to the parking.
So while returning he has to travel (x+3.25) miles
Total distance = 2x+3.25 miles
time equation = (2x+3.25)miles*8mins/miles = 50 mins
solving for x, we get it as 1.5 miles

khairilthegreat · Answer

Bob has only 50 minutes to complete the whole run. With rate of 8 minutes/mile the distance he can cover is 50/8 mile.

We can picture the path as follow

Running south
<-------3.25 miles--------><---- d = ? ----->

Running north back to origin
<-------3.25 miles--------><------- d ------->

From this we can conclude if he want to go back to his first point the distance would be d + d + 3.25.

Because he only has 50/8 mile left, we can make equation as follows d+d+3.25 = 50/8; 2d+3.25 = 6.25 --> d=1.5

jalpagandhi · Answer

1. He runs 3.25 mile down the south. 
2. Then he runs 6.25miles in 50 min. (i.e. 50/8). 
So he runs 3.0 miles in North direction. (6.25 total - 3.25 south). 
Hence his one-way trip in North is 1.5miles. (3.0/2).

ronr34 · Answer

He runs 3.25 south.
Now we know he has only 6.25-3.25 to run (as 3.25 is already reserved for going back to the parking lot)
so we have 3 miles left, to get back to where he is now.... divide that by 2, and get 1.5 left in each direction

SVaidyaraman · Answer

1. Converting speed to miles / minute, speed =1/8 miles/minute
2. Miles run = 3.25
3. To cover 3.25 miles in the return he needs 3.25/(1/8) minutes = 26 min
4. In the remaining 24 minutes, down south is 12 min and up north is 12 minutes
5. So down south further, he can run 12*1/8 = 1.5 miles

ms1862 · Answer

ScottTargetTestPrep

Do you mind explaining this?

ScottTargetTestPrep · Answer

Solution: I have actually posted a solution for this question (which can be found at https://gmatclub.com/forum/after-drivin ... l#p1680552), here’s an alternate solution: Suppose that Bob can run x miles further and make it back in 50 minutes (in total). This means that he will run x miles and turn around to run x + 3.25 miles for a total of x + x + 3.25 = 2x + 3.25 miles in 50 minutes. We are given that Bob can run 1 mile in 8 minutes, so 2x + 3.25 miles will take him (2x + 3.25)*8 minutes. We want this quantity to equal 50, hence we can create the following equation: (2x + 3.25)*8 = 50 2x + 3.25 = 50/8 = 6.25 2x = 6.25 - 3.25 = 3 x = 1.5 So, Bob can run 1.5 miles further if he is to run for 50 more minutes. Answer: A

GMATinsight · Answer

Answer: Option A

Video solution by  GMATinsight

https://www.youtube.com/watch?v=ASrkJck_0DA

Ruzz2 · Answer

Distance = speed ×time. So why have they done distance = time ÷ speed in some solutions? 
12mins ÷ 8mins/mile? Why is it done in this way can someone explain?

Posted from my mobile device

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=NbMCDG1c0Os

BrentGMATPrepNow · Answer

Let's sketch the situation: 
 https://i.imgur.com/TDh7FP2.png

If we let   x   = the extra distance Bob jogs south, then.....
 https://i.imgur.com/k7mzMYv.png 
... he must travel the same   x   miles north PLUS the additional   3.25   miles.

So the total distance Bob travels (AFTER jogging 3.25 miles south) =   x   +   x   +   3.25   miles
=   2x + 3.25   miles.

Since Bob's jogging speed is 8 minutes per mile, we can say that he travels 1 mile in 8 minutes. 
So his speed = distance/time =   1/8   miles per minute. 
Finally, Bob wants his remaining travel time to be 50 minutes.

Remaining travel time = (remaining distance)/(jogging speed) 
Plug in our values to get:  50 =  (  2x + 3.25  )/(  1/8  )
Simplify:  50 = (2x + 3.25)(8) 
Expand:  50 = 16x + 26 
Subtract 26 from both sides:  24 = 16x 
Solve:  x = 24/16 = 3/2 = 1.5

So, Bob can run an additional 1.5 miles.

Answer: A

AbhiDeb · Answer

first thing you want to do is convert his speed:

given speed - 8 min/mile
converted - 1/8 miles/min

He has only 50 mins more to run at this speed, thus:

distance to be covered: Speed x Time : 50 x 1/8 =  6.25 miles

Now, total distance = 3.25 + 6.25 =  9.5 miles

This is his distance covered north and south equally. Thus one way distance would be half of this - 9.5/2 = 4.75

Thus the distance that is remaining to be covered south = 4.75 - 3.25 =  1.5  -  Answer @

findingmyself · Answer

Time taken to cover 3.25 miles at 8 minutes/mile
8 minutes/mile=1/8 mile/minute
Time taken for 3.25 miles= 3.25/(1/8)=26 minutes
Balance time =24 minutes
Miles covered in 24 minutes =3 miles
Since its to and fro: Divide 3 miles by 2
Answer= 1.5 miles

After driving to a riverfront parking lot, Bob plans to run

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After driving to a riverfront parking lot, Bob plans to run

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