Bob and Wendy walk to restaurant

[hk]

I got this question from MGMAT cat. I'm not satisfied with their method of solving as it could take more than 2 mins. Can anybody point out a logical way of solving such questions quickly?

Bob and Wendy planned to walk from their home to a restaurant for dinner together. However, Bob was delayed at work, and Wendy left for the restaurant before Bob did. If the restaurant is 3 miles from their home and Bob left for the restaurant a half-hour after Wendy did, how long did Wendy have to wait for Bob at the restaurant?

(1) Wendy walked at a constant pace of 4 miles per hour

(2) Bob walked at a constant pace of 1 mile per hour faster than Wendy.

OA after some discussion.

[Feep]

Well, the question gives us the "head-start" time (fairly irrelevant) and the distance away, 3 miles.

(1) gives a specific rate for Wendy, but Bob could race there like an Olympic sprinter or take his sweet old time. Who knows how long she could be waiting? Insufficient.

(2) gives a statement that puts their relative velocities into perspective. If you're unsure about the mathematics behind this stuff, as many are, just go ahead and plug in some numbers and see what you get. 3 miles away, 3 mph seems like a good number:

Bob = 3 mph, Wendy = 2 mph, Bob's Trip = 1 hour, Wendy's Trip = 90 minutes, so they actually arrive at the same time. No wait.

Bob = 4 mph, Wendy = 3 mph, Bob's Trip = 45 min, Wendy's Trip = 60 min, so Wendy has to wait 15 minutes.

This is all the information given, and so (2) is insufficient.

Together, however, we have definite speeds for each party. Sufficient.

C.

[hk]

thanks a lot feep..

I actually followed the same procedure but my mistake was that i use the values 4 and 3 for their speed and since i could find the wait time i presumed that this is sufficient (statement 2). Now i have learnt that i should always substitute 2 sets of values, always!!!

thanks again..