Bunuel wrote:
At the same time Sue began rolling a wheelbarrow from X to Y, Nancy started walking along the same road from Y to X. If Sue's traveling rate was 2 feet per second and Nancy's was 3 feet per second, and if the wheelbarrow wheel rolled without slipping, what is the radius of the wheel on Sue's wheelbarrow?
(1) At the moment Sue and Nancy crossed paths, Sue had traveled 60 feet with the wheelbarrow.
(2) The total number of wheel revolutions during Sue's trip from X to Y was 75.
MANHATTAN GMAT OFFICIAL SOLUTION:For the wheelbarrow, we can set up a distance formula:
Distance Traveled = (Wheel Circumference) (Number of Wheel Revolution)
Distance Traveled = (2πr) (Number of Wheel Revolutions)
\(\frac{Distance \ Traveled}{(2\pi{r})(Number \ of \ Wheel \ Revolutions)}=r\)
We can rephrase the question from “What is r?” to “What is the distance traveled and the number of wheel revolutions?”
(1) INSUFFICIENT: This provides the distance traveled, but no information about the number of wheel revolutions.
(2) INSUFFICIENT: This gives the number of wheel revolutions, but no information about the total distance from X to Y.
(1) AND (2) SUFFICIENT: If Sue traveled 60 feet at a rate of 2 feet per second, she traveled for 60/2 = 30 seconds before meeting Nancy. During those 30 seconds, Nancy had traveled at a rate of 3 feet per second, for a distance of (3)(30) = 90 feet. The total distance between X and Y is 60 + 90 = 150 feet.
We also know the total number of wheel revolutions that occurred between X and Y, so we have the answer to the rephrased question.
The correct answer is C.