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Rate time and distance

by leonswati » Fri Sep 16, 2011 10:39 am
Angela begins walking at 4 mph around a circular track with a radius of 8 miles. Exactly 5 hours later, Matt leaves from the same point in the opposite direction jogging at 6 mph. For how many hours will Angela have been walking when Matt has passed and moved 10 miles beyond her?
1.6Ï€ - 1
2.6Ï€ + 4
3.2Ï€ - 1
4.6Ï€ - 2
5.6Ï€ - 2

Plz solve it.... I think the answer is 3 But I am not sure...
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by gmatclubmember » Fri Sep 16, 2011 11:10 am
leonswati wrote:Angela begins walking at 4 mph around a circular track with a radius of 8 miles. Exactly 5 hours later, Matt leaves from the same point in the opposite direction jogging at 6 mph. For how many hours will Angela have been walking when Matt has passed and moved 10 miles beyond her?
1.6Ï€ - 1
2.6Ï€ + 4
3.2Ï€ - 1
4.6Ï€ - 2
5.6Ï€ - 2

Plz solve it.... I think the answer is 3 But I am not sure...
After 5 hours Angela would have walked 20 miles (5*4).
Lets say after t hours she met with Matt so...
20+4t+6t=2PI*8
t=8PI/5-2.
Relative speed of them going away from each other is 10 miles per hour (4+6). So they would be 10 miles apart after one hour of crossing each other.
Total time for which matt have been walking would be t+1 hours
t=8PI/5-2+1=8PI/5-1.
NB: I guess the radius of the circle is a typo ( it should be 10 for answer choice C).

Cheers
Ami/-
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by leonswati » Fri Sep 16, 2011 11:27 am
I am very sorry.... The answer choices I typed were wrong.Let me type the question again.... Angela begins walking at 4 mph around a circular track with a radius of 8 miles. Exactly 5 hours later, Matt leaves from the same point in the opposite direction jogging at 6 mph. For how many hours will Angela have been walking when Matt has passed and moved 10 miles beyond her?
1. 1.6Ï€ - 1
2. 1.6Ï€ + 4
3. 2Ï€ - 1
4. 2.6Ï€ - 2
5. 3.6Ï€ - 2

According to you It should be B then...
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by sl750 » Fri Sep 16, 2011 11:28 am
Angela covers a distance of D=5*4 =20m in the time that Matt leaves his place.

Distance of the track is = 16pi
Remaining distance to cover = 16pi-20

As both Angela and Matt are walking towards each other, we add the rates

We also know that an additional distance of 10m is covered once after they cross each other
D = 16pi-20+10 = 16pi-10

T=(16pi-10)/10 = (8pi-5)/5. To find Angela's time add the 5 hours to this result. The answer doesn't seem to match

Even if I take the radius as 10miles. I get a time of 2pi+4 hrs

What is the source of this question?
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by sl750 » Fri Sep 16, 2011 11:31 am
B looks good. Just saw your reply

(8pi-5)/5 = 1.6pi-1+5 = 1.6pi+4
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by leonswati » Fri Sep 16, 2011 11:39 am
The source is the practice test 4 in the kaplan website, however the same question set is also available at https://www.scribd.com/doc/58005404/GMAT ... et-4-Quant
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by aplavakarthik » Fri Sep 16, 2011 11:48 am
Hi,

options D & E are same....I have googled for the question to check the right options are these are the right options.

a. 1.6pi-1
b. 1.6pi+4
c. 2pi-1
d. 2.6pi-2
e. 3.6pi-2

So here is my solution, radius of the circular track is 8 so the circumference is 16pi = 48(approx)
Now for mat to cross Angela by 10 miles they should travel a total of 48+10=58 km.(since in Matt starts in opposite direction they ll meet before Angela reaches to start point.)

Now the question is in how much time will it take for them to travel 38 miles(since Angela has already covered 20miles before Matt started)
38/10 = 3.8(10 because they together cover 10miles per hour)

It takes Angela 8.8 hours total. It ll go with option b/e

Imo b/e.

i ll go with e
Last edited by aplavakarthik on Fri Sep 16, 2011 11:57 am, edited 2 times in total.
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by GMATGuruNY » Fri Sep 16, 2011 11:50 am
leonswati wrote:Angela begins walking at 4 mph around a circular track with a radius of 8 miles. Exactly 5 hours later, Matt leaves from the same point in the opposite direction jogging at 6 mph. For how many hours will Angela have been walking when Matt has passed and moved 10 miles beyond her?
� ≈ 3.
Circumference of the track = 2�r = 2�*8 ≈ 48 miles.
In 5 hours, distance traveled by Angela = r*t = 4*5 = 20 miles.
Remaining distance = 48-20 = 28 miles.
Since 10 more miles must be traveled after Matt meets Angela, the total distance to be traveled by Matt and Angela together = 28+10 = 38 miles.
When elements travel toward each other, they work together to cover the distance between them, so we add their rates.
Combined rate for Matt and Angela = 4+6 = 10 miles per hour.
Time to travel 38 miles = d/r = 38/10 = 3.8 hours.

Total time that Angela walks = 5+3.8 = 8.8 hours.

Here is the correct set of answer choices:

Image

Answer choice B = 1.6� + 4 ≈ (1.6)*3 + 4 = 8.8.
Answer choice E = 3.6� - 2 ≈ (3.6)*3 - 2 = 8.8.

The circumference is 16�.
To calculate the number of hours for which Matt and Angela both travel, a portion of this circumference must be divided by Matt and Angela's combined rate of 10mph.
Thus, the correct answer must contain (16�)/10 = 1.6�.

The correct answer is B.

For the skeptical:
Distance to be traveled by Matt and Angela together = circumference - distance traveled by Angela alone + 10 extra miles = 16� - 20 + 10 = 16� - 10.
Time for Matt and Angela to travel this distance = d/r = (16� - 10)/10 = 1.6� - 1.
Total time for Angela = 5 + (1.6� - 1) = 1.6� + 4.
Last edited by GMATGuruNY on Fri Sep 16, 2011 12:50 pm, edited 4 times in total.
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by aplavakarthik » Fri Sep 16, 2011 11:56 am
GMATGuruNY wrote:
leonswati wrote:Angela begins walking at 4 mph around a circular track with a radius of 8 miles. Exactly 5 hours later, Matt leaves from the same point in the opposite direction jogging at 6 mph. For how many hours will Angela have been walking when Matt has passed and moved 10 miles beyond her?
1.6Ï€ - 1
2.6Ï€ + 4
3.2Ï€ - 1
4.6Ï€ - 2
5.6Ï€ - 2

Plz solve it.... I think the answer is 3 But I am not sure...
� ≈ 3.
Circumference of the track = 2�r = 2�*8 ≈ 48 miles.
In 5 hours, distance traveled by Angela = r*t = 4*5 = 20 miles.
Remaining distance = 48-20 = 28 miles.
Since 10 more miles must be traveled after Matt meets Angela, the total distance to be traveled by Matt and Angela together = 28+10 = 38 miles.
When elements travel toward each other, they work together to cover the distance between them, so we add their rates.
Combined rate for Matt and Angela = 4+6 = 10 miles per hour.
Time to travel 38 miles = d/r = 38/10 = 3.8 hours.

Total time that Angela walks = 5+3.8 = 8.8 hours.

Only answer choice C comes close:
3.2�-1 ≈ 8.6.

The correct answer is C.
8.8 is right. but its not 3.2pi-1 it is 3. 2pi-1

b and e gives u 8.8 when calculated
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by GMATGuruNY » Fri Sep 16, 2011 12:42 pm
aplavakarthik wrote:
GMATGuruNY wrote:
leonswati wrote:Angela begins walking at 4 mph around a circular track with a radius of 8 miles. Exactly 5 hours later, Matt leaves from the same point in the opposite direction jogging at 6 mph. For how many hours will Angela have been walking when Matt has passed and moved 10 miles beyond her?
1.6Ï€ - 1
2.6Ï€ + 4
3.2Ï€ - 1
4.6Ï€ - 2
5.6Ï€ - 2

Plz solve it.... I think the answer is 3 But I am not sure...
� ≈ 3.
Circumference of the track = 2�r = 2�*8 ≈ 48 miles.
In 5 hours, distance traveled by Angela = r*t = 4*5 = 20 miles.
Remaining distance = 48-20 = 28 miles.
Since 10 more miles must be traveled after Matt meets Angela, the total distance to be traveled by Matt and Angela together = 28+10 = 38 miles.
When elements travel toward each other, they work together to cover the distance between them, so we add their rates.
Combined rate for Matt and Angela = 4+6 = 10 miles per hour.
Time to travel 38 miles = d/r = 38/10 = 3.8 hours.

Total time that Angela walks = 5+3.8 = 8.8 hours.

Only answer choice C comes close:
3.2�-1 ≈ 8.6.

The correct answer is C.
8.8 is right. but its not 3.2pi-1 it is 3. 2pi-1

b and e gives u 8.8 when calculated
I was able to track down what I think is the correct set of answer choices. Please see my amended post above.
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by aplavakarthik » Fri Sep 16, 2011 10:57 pm
Now this looks in good shape.

I ll now go with B.

IMO B
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by saisree » Sat Sep 17, 2011 12:37 pm
Hi Mitch,

I have a question. Here the question is how long Angela has been walking - condition Matt has crossed her and moved 10 miles further. So the total distance travelled by her and hence the time taken can be sectioned into 3 parts.

Part 1 - time taken to travel the distance where Angela walked alone (initial 5 hours)
Part 2 - time taken to travel the distance when Angela and Matt where walking toward each other
Part 3 - time taken to travel the distance after Matt crossed and moved 10 miles further (this will be equal to the time taken for Matt to travel 10 miles at a speed of 6 mph)

Part 1 + Part 2 + Part 3 = 5 + (16pi-20)/10 + 10/6

I did not understand why we were adding the 10 miles along with 16pi-20 to get the total time. Because we are asked about the total time Angela has travelled even after Matt has crossed her and moved 10 miles further.

Please let me know if my approach is wrong.
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by GMATGuruNY » Sat Sep 17, 2011 12:49 pm
saisree wrote:Hi Mitch,
Part 3 - time taken to travel the distance after Matt crossed and moved 10 miles further (this will be equal to the time taken for Matt to travel 10 miles at a speed of 6 mph)
For how many hours will Angela have been walking when Matt has passed and moved 10 miles beyond her?

The question above implies that Angela, like Matt, continues to walk after the two meet.
Thus, the 10 miles traveled after the two meet must be divided by the COMBINED rate for Angela and Matt.
Last edited by GMATGuruNY on Sat Sep 17, 2011 12:59 pm, edited 1 time in total.
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by saisree » Sat Sep 17, 2011 12:57 pm
aaaah...yes i get it now.....you are right.....thanks a lot Mitch for your patience to explain.....
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