For this problem we can set up an RTD (rate x time = distance) chart for Bob and Wendy. The difficulty is that Bob and Wendy will be traveling the same distance — it is the amount of time that each will be traveling is unknown.

One way that we can get around this problem is by assigning two different variables for time: one for the amount of time that they are both walking (let's say t), and a second for the amount of time that only Bob is walking (in other words, for the amount of time that Wendy is waiting.) Let's call that variable x. The question, rephrased, is "What is x?" In addition, we may want to "link" Bob and Wendy's rates to see whether the difference in the rates is sufficient. To do that, instead of assigning variables for Bob and Wendy's rates separately, we should assign a variable for Wendy's rate (rw) and a second variable for the difference between Bob and Wendy's rates (y). Bob's rate is then rw + y:

Bob Wendy

R rw + y rw

T t + x t + 1/2

D 3 3

Since rate x time = distance, we have:

(rw + y)(t + x) = 3

rw(t+1/2) = 3

Since they are traveling the same distance, we can set up the equations equal to each other and solve for x.

(rw + y)(t + x) = rw(t+1/2)

rwt + yt + xy + rwx = rwt + 1/2rw

yt + xy + rwx = 1/2rw

x(y + rw) = 1/2rw – yt

x = (1/2rw – t)/(rw + y)

Indeed the difference in rates is not sufficient. Therefore the question can be expressed/rephrased as follows:

What are Wendy's rate and the difference between Bob and Wendy's rate? (Or alternately, what are Bob and Wendy's individual rates?) Note that we can calculate t whenever we know Wendy's rate.

(1) INSUFFICIENT: This statement does not tell us anything about Bob's speed.

(2) INSUFFICIENT: As we saw earlier, knowing the difference between the rates is insufficient. We need to know both of Bob's and Wendy's rates.

(1) and (2) SUFFICIENT: Based on the formula above, x = [1/2(4) – 1·t]/[4 + 1] = (2 – t)/5

But since rw(t+1/2) = 3 and rw = 4, we know that t = 1/4. Therefore x = (2 – 1/4)/5 = 7/20 hours, or 21 minutes.

The correct answer is C.

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Just chk once ... i have just copied and pasted it here.

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