Friends Part

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) R2 – 4


If we want Brenda’s distance to be twice as great as Alex’s distance, we can set up the following equation: 

2(4T) = R(T – 1), where 4T is Alex’s distance (rate Ч time) and R(T – 1) is Brenda’s distance (since Brenda has been traveling for one hour less). 

If we simplify this equation to isolate the T (which represents Alex’s total time), we get: 

2(4T) = R(T – 1)
8T = RT – R
R = RT – 8T
R = T(R – 8)


R – 8

This is choice C.

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