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Timothy leaves home for school, riding his bicycle

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Timothy leaves home for school, riding his bicycle [#permalink] New post 02 Sep 2012, 14:59
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Question Stats:

72% (02:56) correct 28% (02:13) wrong based on 134 sessions
Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 36 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?

A) 1/3
B) 3
C) 4
D) 9
E) 12

I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanation :) Thanks
[Reveal] Spoiler: OA

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Re: Timothy leaves home for school, riding his bicycle [#permalink] New post 02 Sep 2012, 19:41
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Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen
minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and
immediately leaves home to bring it to him. If his mother drives at 36 miles per hour, how far
(in terms of miles) must she drive before she reaches Timothy?

A) 1/3

B) 3

C) 4

D) 9

E) 12

Suppose Timothy's mom meets him after time 't'

Then distance traveled by his mom = distance traveled by him in (15mins) + distance traveled by him in time 't'

=> 36 * t = 9 *(15/60) + 9*t
=> t = (1/12) hrs

Distance traveled = 36 * t = 36 * (1/12) miles = 3miles

So, Answer will be B

And am not sure about the tag but i guess 600-700 is fine.

Hope it helps!
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Re: Timothy leaves home for school, riding his bicycle [#permalink] New post 23 Aug 2014, 19:51
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Re: Timothy leaves home for school, riding his bicycle [#permalink] New post 10 May 2015, 02:58
9*1/4=9/4 miles Timothy ran before his mom started

36-9=27m/h is a rate to achieve Timothy

9/4:27=1/12 h is a time mom will run

36*1/12=3 miles mom need to run

B
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Re: Timothy leaves home for school, riding his bicycle [#permalink] New post 10 May 2015, 15:32
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Hi All,

Sometimes these types of Combined Rate/Chase-Down questions can be really complicated, but this one is not so bad. You can actually solve it with some logic and a little bit of math (and avoid the longer calculation-heavy approach).

Based on what we're told in the prompt, we know that Timothy travels on his own at 9mph for 15 minutes. Since 15 minutes = 1/4 of an hour, Timothy traveled 2.25 miles before his Mom gets in the car to chase him down.

Since the Mom drives 36mph and Timothy is only going 9mph, she is traveling 4 TIMES FASTER than he is. In basic terms, this means that for every 1 mile Timothy travels, his Mom travels 4 miles.

So, if Timothy DID travel another 1 mile, he'd have traveled 2.25 + 1 = 3.25 miles while his Mom would have driven 4 miles (and gone past him). This means that his Mom caught him at some point between 2.25 miles and 3.25 miles. There's only one answer that 'fits'....

Final Answer:
[Reveal] Spoiler:
B


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Re: Timothy leaves home for school, riding his bicycle [#permalink] New post 10 May 2015, 21:29
Expert's post
carcass wrote:
Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 36 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?

A) 1/3
B) 3
C) 4
D) 9
E) 12

I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanation :) Thanks


This is a simple relative speed question. Here is a conceptual post on relative speed: http://www.veritasprep.com/blog/2012/07 ... elatively/

Distance Timothy covers in 15 mins i.e. 1/4 hours = Rate*Time = 9/4 miles
Time taken by mom to meet him = Distance/Relative Speed = (9/4)/(36 - 9) = 1/12 hours
Distance traveled by mom in this time = 36 * (1/12) = 3 miles
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Re: Timothy leaves home for school, riding his bicycle [#permalink] New post 11 May 2015, 01:42
Expert's post
In Time, Speed and Distance problems, it's a good idea to draw a rough diagram to visualize the given information.

Image

Let the distance between the Home and the Point of Meeting be D miles. The question asks us to find the value of D.

As per the question, Timothy's mother left home 15 minutes after he did. But they both reached the Point of Meeting at the same time.

This means,

(Time taken by Timothy's mother to cover D miles) = (Time taken by Timothy to cover D miles) - (15 minutes)

Now, \(Time = \frac{Distance}{Speed}\)

So, the above equation becomes:

\(\frac{D}{36} = \frac{D}{9} - \frac{15}{60}\)

Upon solving this, we get, D = 3 miles

One important point to be careful of in Distance and Speed questions is: Use the same units for a particular quantity throughout the question. By this I mean, if the speed is expressed in miles per hour and travel time/ difference between time taken by 2 people is given in minutes, then you must remember to either convert the time from minutes to hours or convert the speed from miles per hours to miles per minutes. Throughout the question, you should use only one unit for time.

Hope this helped! :)

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Re: Timothy leaves home for school, riding his bicycle   [#permalink] 11 May 2015, 01:42
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