enigma123 wrote:

Alex and 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 will have been walking when Brenda has covered twice as much distance as Alex?

A. R-4

B. R/(R+4)

C. R/(R-8)

D. 8/(R-8)

E. 2R - 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

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