Working alone at their respective constant rates, machine A and machine B

BTGModeratorVI wrote: ↑

Wed Jul 29, 2020 2:47 pm

Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?

A: 1/2
B: 3/4
C: 1
D: 1 1/4
E: 1 1/2

Answer: C
Source: GMAT prep

One approach is to assign a "nice value" to the job.
That is, a value that works well with the given information of 3 hours and 6 hours
So let's say the order consists of making 18 widgets

Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively
In other words, Machine A can make 18 widgets in 3 hours, which means Machine A's RATE = 6 widgets per hour
This also tells us that Machine B can make 18 widgets in 6 hours, which means Machine B's RATE = 3 widgets per hour

If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?
COMBINED rate = 6 + 3 = 9 widgets per hour

We want to fill 1/2 the order.
1/2 of 18 widgets is 9 widgets
So we want to make 9 widgets

time = output/rate
So, time = 9/9 = 1 hour

Answer: C

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Jul 29, 2020 2:47 pm

Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?

A: 1/2
B: 3/4
C: 1
D: 1 1/4
E: 1 1/2

Answer: C

Solution:

We see that rates of machines A and B are 1/3 and 1/6, respectively. Therefore, their combined rate is 1/3 + 1/6 = 1/2, and so it will take (1/2) / (1/2) = 1 hour to fill 1/2 of the order.

Answer: C