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# 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 [#permalink]

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06 Dec 2012, 08:19
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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
[Reveal] Spoiler: OA

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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06 Dec 2012, 08:28
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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

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 .

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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11 Jan 2013, 22:02
How do we know that he ran half the distance south ? Thanks

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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12 Jan 2013, 04:52
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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

shahir16 wrote:
How do we know that he ran half the distance south ? Thanks

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

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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23 Feb 2013, 06:27
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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

Last edited by nave on 13 Sep 2013, 15:40, edited 1 time in total.

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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12 Sep 2013, 20:25
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JesseWhelan 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

shahir16 wrote:
How do we know that he ran half the distance south ? Thanks

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

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

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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13 Sep 2013, 12:27
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

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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18 Sep 2013, 05:35
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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

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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29 Oct 2013, 12:25
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).

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After driving to a riverfront parking lot, Bob plans to run [#permalink]

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03 Nov 2013, 21:53
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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

Last edited by ronr34 on 28 Aug 2014, 12:22, edited 1 time in total.

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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06 Nov 2013, 19:07
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?

If bob runs at a constant 8 minutes/mile, then he will have ran for 26 minutes by the time he travels 3.25 miles. If he decided to run for another 50 minutes that means he traveled for 76 minutes total, half of which will be spent going south and the other half, going north. 76/2 = 38. 38/8 = 4.75...the distance he traveled from north to south then from south to north again. 4.75-3.25 = 1.5 (the distance he will travel past 3.25 miles before he turns around.

(A) 1.5

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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15 Jul 2014, 00:23
Pls confirm if both the below formula is correct :
1. Rate*time = distance, where rate is expressed as distance per unit time
2. Rate*distance= time, where rate is expressed as time per unit distance

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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15 Jul 2014, 02:34
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kshitij89 wrote:
Pls confirm if both the below formula is correct :
1. Rate*time = distance, where rate is expressed as distance per unit time
2. Rate*distance= time, where rate is expressed as time per unit distance

Posted from my mobile device

Hi Kshitij89,

This is a bit worrisome that you are asking about these formulas. You don't need to remember and you shouldn't rely on these formulas.

The dependence on formulas indicate that you probably don't understand the basis of these formulas because once you understand the basis or the fundamentals, the need for the formulas goes away.

We know that rate in this question is used as a synonym for speed.

We know that speed = distance/time

So, distance = speed*time OR rate*time

If you change the definition of rate, of course the formula will change. However, for sure, you don't need to remember the formula, you just need to understand the basis from where the formula is coming from.

For example, the formula: distance = rate*time is coming directly from the definition of speed (or rate). Once you understand this, you don't need to remember this formula.

You just need to know speed is defined as distance/time and I think remembering this would be very natural to you unlike other formulas.

Math is about common sense and an interpretation or representation of reality. It is not at all about dead formulas and equations.

AEL

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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15 Jul 2014, 06:33
Hi AEL,

My confusion was in context to the present question as here the rate was expressed as 'time/distance'. I was not able to apply the general formula though was able to solve by deciphering the sentences.

So I was really confused as how the formula is used here. Hope you understand what I meant. Let me know if you have any further explanation which will help me out.

Regards
Kshitij

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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15 Jul 2014, 22:31
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kshitij89 wrote:
Hi AEL,

My confusion was in context to the present question as here the rate was expressed as 'time/distance'. I was not able to apply the general formula though was able to solve by deciphering the sentences.

So I was really confused as how the formula is used here. Hope you understand what I meant. Let me know if you have any further explanation which will help me out.

Regards
Kshitij

Hi Kshitij,

Got you

If you are able to solve a question just by understanding the sentences, then you are good enough No need to worry about the formulas.

Now, as you said, in this case, the rate was defined as

Rate = time/distance.

Now, if you multiple both sides by distance, you get

Rate*distance = time.

AEL

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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16 Jul 2014, 09:00
Hi AEL,

The general formula is Rate*Time = Distance whereas the one used is different. So I was stuck in the ambiguity of the formula as how can the general formula be wrong

Thanks
Kshitij

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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22 Aug 2014, 10:59
Is there a location where I can find similar very very wordy problems? Not necessarily rate related, but those are fine as well.

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After driving to a riverfront parking lot, Bob plans to run [#permalink]

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22 Aug 2014, 11:28
For the first 3.25 miles, Bob takes 3.25x8=26minutes

Say he runs 'x' miles further south. So the total distance he covers is (3.25+2x+3.25) in (50+26) minutes
So we have 6.5+2x=76/8 => x=1.5

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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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23 Aug 2014, 11:14
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russ9 wrote:
Is there a location where I can find similar very very wordy problems? Not necessarily rate related, but those are fine as well.

Check Word Problems in our Questions Banks: viewforumtags.php
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Re: After driving to a riverfront parking lot, Bob plans to run [#permalink]

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11 Sep 2014, 04:41
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

8 minutes /mile for 50 minutes then for 50 minutes he ran for 6.25 miles.

6.25 also cover the distance 3.25 which he already covered . 6.25-3.25 = 3

after 3.25, his to & fro has to be 3/2 =1.5..

question took lot of time to understand. once i imagine the scenario , i got it

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Re: After driving to a riverfront parking lot, Bob plans to run   [#permalink] 11 Sep 2014, 04:41

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