Jack works at a constant rate and he can produce a maximum of 5 units of a product in 4 hours. He is paid $4 per unit...

AAPL wrote: ↑

Wed Jan 20, 2021 9:33 am

E-GMAT

Jack works at a constant rate and he can produce a maximum of 5 units of a product in 4 hours. He is paid $4 per unit, for the first 20 units and $5.5 for each additional unit, that he produces on a particular day. If he earned $91 on the first day and $135 of the second day, what is the minimum time that Jack had worked on these two days combined?

A. 17 hours 36 minutes
B. 39 hours 12 minutes
C. 41 hours 36 minutes
D. 42 hours
E. 44 hours

OA C

Solution:

For the first 20 units Jack produces, he earns 20 x 4 = $80. Since he earns $5.50 per unit after the first 20 units, he must have produced (91 - 80) / 5.5 = 2 additional units on the first day and (135 - 80) / 5.5 = 10 additional units on the second day. In other words, he produced 20 + 2 = 22 units on the first day and 20 + 10 = 30 units on the second day. Since he produced 22 + 30 = 52 units on both days and his maximum rate is 5/4 units per hour, the minimum time that Jack worked on these two days combined is 52 / (5/4) = 52 x 4/5 = 41.6 hours, or 41 hours 36 minutes.

Answer: C