Speed & distance Problem 4

[aditiniyer]

Alex & Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R>8, which of the following represents the amount of time in terms of R, that Alex would have been walking when Brenda would has covered twice as much distance as Alex?

1) R-4
2) R/(R+4)
3) R/(R-8)
4) 8/(R-8)
5) R^2 - 4

[GMATGuruNY]

Alex & Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R>8, which of the following represents the amount of time in terms of R, that Alex would have been walking when Brenda would has covered twice as much distance as Alex?

1) R-4
2) R/(R+4)
3) R/(R-8)
4) 8/(R-8)
5) R^2 - 4

Let R = 16mph.
We can PLUG IN THE ANSWERS, which represents Alex's time.

Answer choice C: R/(R-8) = 16/(16-8) = 2 hours.
At a rate of 4mph, the distance traveled by Alex in 2 hours = 4*2 = 8 miles.
Since Brenda starts to bike 1 hour after Alex starts to walk, Brenda bikes for 1 hour.
At a rate of 16mph, the distance traveled by Brenda in 1 hour = 16*1 = 16 miles.
Success!
Brenda's distance is twice Alex's distance.

The correct answer is C.

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Hi aditiniyer,

This question can be solved by TESTing VALUES.

We're told that Alex walks 4 miles per hour and, an hour later, Brenda starts biking at R miles per hour.

Let's say that Alex walks for 2 HOURS; that would be 8 total miles. The question asks us to focus on Brenda's travel covering TWICE Alex's distance, so we can build all of our work around the two hours that Alex traveled.

Alex = 2 hours, 8 total miles
Brenda = 1 hour, 16 total miles

Although the prompt doesn't clearly state it, it asks for the total number of hours that Alex traveled at the point that Brenda had traveled twice Alex's distance. Thus, we're looking for an answer that equals 2 when R = 16.

Answer A: 12 NOT a match
Answer B: 16/20 NOT a match
Answer C: 16/8 = 2 This IS a match
Answer D: 8/8 = 1 NOT a match
Answer E: 16^2 - 4 = NOT a match

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[DavidG@VeritasPrep]

Alex & Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R>8, which of the following represents the amount of time in terms of R, that Alex would have been walking when Brenda would has covered twice as much distance as Alex?

1) R-4
2) R/(R+4)
3) R/(R-8)
4) 8/(R-8)
5) R^2 - 4

We can also do some good old-fashioned algebra
Alex: If her rate is 4mph, and she walks for t hours, she'll cover 4t miles.
Brenda: Her rate is R mph and she starts an hour later, so she's traveling for t-1 hours. She'll cover R(t-1) miles

If Brenda covers twice the distance that Alex has covered, then R(t-1) = 2*4t

Simplify:
Rt - R = 8t
Rt - 8t = R
t(R - 8) = R
t = R/(R-8); The answer is C

[Scott@TargetTestPrep]

Alex & Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R>8, which of the following represents the amount of time in terms of R, that Alex would have been walking when Brenda would has covered twice as much distance as Alex?

1) R-4
2) R/(R+4)
3) R/(R-8)
4) 8/(R-8)
5) R^2 - 4

We are given that Alex has a rate of 4 mph and Brenda has a rate of R mph. We are also given that Alex begins to walk away from Brenda in a straight line at a rate of 4 mph. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction. Thus, we can let Alex's time = T + 1 and Brenda's time = T.

Finally, since distance = rate x time, Alex's distance = 4(T + 1) = 4T + 4 and Brenda's distance = RT. We need to determine the amount of time it takes Brenda to cover twice the distance Alex has gone. So, we can create the following equation and determine T:

2(4T + 4) = RT

8T + 8 = RT

8 = RT - 8T

8 = T(R - 8)

8/(R - 8) = T

Since we are asked for Alex's time, T + 1 = 8/(R - 8) + (R - 8)/(R - 8) = R/(R - 8).

Answer: C