GMAT prep Rate Problem

[gdrea3]

While working alone at the their respective rates, machine X produces 240 files in 4 hours and machine Y produces 240 files in 8 hours. How long would it take the two working at their respective rates to process 240 files?

A) 2 hours
B) 2 hours 20 min
C) 2 hours 40 min
D)6 hours
E) 6 hours 20 min

Answer: C
I'm usually good w/rate problems but had no idea how to do this one! Thanks!

[mals24]

Just treat this like a usual work/rate question.

The question tells you x alone can do the job in 4 hrs and y alone in 8 hrs. How much time will they take to do the job together?

The amount of work they do together = 1/x+1/y=(x+y)/xy= (4+8 )/4*8=3/8

Hence the time taken together = 8/3 = 2 hrs 40 mins

You can also use the formula (xy)/(x+y) directly to find the time taken together.

hence C

[cramya]

240 files in 4 hours

In 1 hour 240/4 = 60

Similarly 240/8 = 30

Working together combine their rates:

(60 * 1(no of first type machines) + 30 *1(no of second machines) ) h = 240

h = 2 6/9 = 2hours 40 mins

[cramya]

You can also use this formula to find the time taken together:

T1*T2/T1+T2

= 4*8 / (4+8)
= 32/12 = 2 HOURS 40 MINS