anilsingh wrote:Bob and Wendy left home to walk together to a restaurant for dinner. They started out walking at a constant pace of 3 mph. At precisely the halfway point, Bob realized he had forgotten to lock the front door of their home. Wendy continued on to the restaurant at the same constant pace. Meanwhile, Bob, traveling at a new constant speed on the same route, returned home to lock the door and then went to the restaurant to join Wendy. How long did Wendy have to wait for Bob at the restaurant?
(1) Bob's average speed for the entire journey was 4 mph.
(2) On his journey, Bob spent 32 more minutes alone than he did walking with Wendy.

For each statement, test TWO CASES.
If Wendy's waiting time is THE SAME in each case, then the statement is SUFFICIENT.
If Wendy's waiting time is NOT THE SAME in each case, then the statement is INSUFFICIENT.

Note the sum of the distances for Bob:
(1/2 the distance from home to the restaurant) + (distance back home) + (distance from home to the restaurant) = TWICE the total distance from home to the restaurant.

Statement 1: Bob's average speed for the entire journey was 4 mph.
Case 1: Let the distance between home and the restaurant = 6 miles.
At a rate of 3mph, the total time for Wendy to travel 6 miles to restaurant = d/r = 6/3 = 2 hours.
At a rate of 4mph, the total time for Bob to travel twice the total distance = 2d/r = (2*6)/4 = 3 hours.
Waiting time for Wendy = 3-2 = 1 hour.

Case 2: Let the distance between home and the restaurant = 12 miles.
At a rate of 3mph, the total time for Wendy to travel 12 miles to restaurant = d/r = 12/3 = 4 hours.
At a rate of 4mph, the total time for Bob to travel twice the total distance = 2d/r = (2*12)/4 = 6 hours.
Waiting time for Wendy = 6-4 = 2 hours.

Since Wendy's waiting time is NOT THE SAME in each case, INSUFFICIENT.

Statement 2: On his journey, Bob spent 32 more minutes alone than he did walking with Wendy.
Case 1: Time for Wendy and Bob together to travel 1/2 the distance between home and the restaurant = 1 minute.
Time for Wendy to travel the remaining 1/2 of the distance = 1 minute.
Since Bob's time alone is 32 minutes longer than the 1 minute he traveled with Wendy, Bob's time to reach the restaurant = 1+32 = 33 minutes.
Waiting time for Wendy = 33-1 = 32 minutes.

Case 2: Time for Wendy and Bob together to travel 1/2 the distance between home and the restaurant = 10 minutes.
Time for Wendy to travel the remaining 1/2 of the distance = 10 minutes.
Since Bob's time alone is 32 minutes longer than the 10 minutes he traveled with Wendy, Bob's time to reach the restaurant = 10+32 = 42 minutes.
Waiting time for Wendy = 42-10 = 32 minutes.

Since Wendy's waiting time is THE SAME in each case, SUFFICIENT.

The correct answer is B.