M7MBA wrote: ↑Sat Dec 18, 2021 6:20 am
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 \(\dfrac12\) of that order?
A: \(\dfrac12\)
B: \(\dfrac34\)
C: \(1\)
D: \(1 \frac14\)
E: \(1 \frac12\)
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
