Work/Rate Problems

[swerve]

A machine that produces stroopwafels operates for four hours. During the first hour the machine works at a constant rate. During the next two hours, it works at double that rate, and during the last hour it works at double its previous rate. If the machine produces X stroopwafels during the three first hours, then during the four hours the machine produces how many stroopwafels?

A. \(\dfrac{4}{5}X\)
B. \(\dfrac{9}{5}X\)
C. \(2X\)
D. \(\dfrac{9}{4}X\)
E. \(\dfrac{7}{3}X\)

The OA is B

Source: Economist GMAT

[Scott@TargetTestPrep]

A machine that produces stroopwafels operates for four hours. During the first hour the machine works at a constant rate. During the next two hours, it works at double that rate, and during the last hour it works at double its previous rate. If the machine produces X stroopwafels during the three first hours, then during the four hours the machine produces how many stroopwafels?

A. \(\dfrac{4}{5}X\)
B. \(\dfrac{9}{5}X\)
C. \(2X\)
D. \(\dfrac{9}{4}X\)
E. \(\dfrac{7}{3}X\)

The OA is B

Source: Economist GMAT

We can let the rate of the machine during the first hour be 10 stroopwafels, and thus, the rate during the next two hour is 20 stroopwafels per hour, and the rate during the last hour is 40 stroopwafels. Therefore, during the first 3 hours, the machine produces 10 + 2 * 20 = 50 stroopwafels. We see that X = 50 and therefore, since the total number of stroopwafels produced during the four hours is 50 + 40 = 90, we see that this is 9/5 * X.

Answer: B