A portable recharging device can recharge 3 batteries at once, and it can charge the batteries while itself being charge

[BTGmoderatorDC]

A portable recharging device can recharge 3 batteries at once, and it can charge the batteries while itself being charged from an outlet. The device can recharge a single dead battery in 3 hours, and it can be completely recharged from an outlet in 2 hours when it contains no batteries. A fully discharged device holding 3 dead batteries is plugged into an outlet. If the capacity of a battery is one-third the capacity of the device, and the device and batteries charge at constant rates, how much time will pass before the device is completely recharged?

a) 5 hours
b) 6 hours
c) 8 hours
d) 9 hours
e) 11 hours


OA B

Source: Princeton Review

[Scott@TargetTestPrep]

A portable recharging device can recharge 3 batteries at once, and it can charge the batteries while itself being charged from an outlet. The device can recharge a single dead battery in 3 hours, and it can be completely recharged from an outlet in 2 hours when it contains no batteries. A fully discharged device holding 3 dead batteries is plugged into an outlet. If the capacity of a battery is one-third the capacity of the device, and the device and batteries charge at constant rates, how much time will pass before the device is completely recharged?

a) 5 hours
b) 6 hours
c) 8 hours
d) 9 hours
e) 11 hours


OA B

Source: Princeton Review

We can let each battery be 1 unit. Since the device charges 1 battery (or 1 unit) in 3 hours, the charge transfer rate from the device to a battery is 1/3 unit/hr and hence that rate is 3/3 = 1 unit/hr when there are 3 batteries in the device.

We are also given that the capacity of a battery is one-third the capacity of the device, so the device is equivalent to 3 batteries, or 3 units. Since it takes 2 hours to charge the device without any batteries, the charge transfer rate from an outlet to the device is 3/2 unit/hr.

Since 3 dead batteries are connected to a discharged device which is connected to an outlet, the charge transfer rate 3/2 - 1 = 1/2 unit/hr. Since the device is equivalent to 3 units, it takes 3/(1/2) = 6 hours to fully charge the device.

Answer: B