A furniture manufacturer has two machines, but only one can

Question

Machine A can complete a certain job in 12 days, working 2 full shifts per day, while Machine B can complete the same job in 15 days, also working 2 full shifts per day. If Machine A works during the first shift each day, Machine B works during the second shift, and both machines work half of the third shift, approximately how many days will it take for Machines A and B to complete the job under this work schedule?

A. 14
B. 13
C. 11
D. 9
E. 7

M06-21

Bunuel · Accepted Answer

Official Solution:

Machine A can complete a certain job in 12 days, working 2 full shifts per day, while Machine B can complete the same job in 15 days, also working 2 full shifts per day. If Machine A works during the first shift each day, Machine B works during the second shift, and both machines work half of the third shift, approximately how many days will it take for Machines A and B to complete the job under this work schedule?

A. 14
B. 13
C. 11
D. 9
E. 7

Machine A requires 12 days * 2 shifts = 24 shifts to complete the entire job;

Machine B requires 15 days * 2 shifts = 30 shifts to complete the entire job;

Each day, both machines work 1.5 shifts ( \frac{3}{2}  shifts). Together, in one day, they complete  \frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}  of the whole job. Therefore, under the current work schedule, they will need approximately  \frac{80}{9} \approx 9  days to finish the entire job.

Answer: D

AleenBola · Answer

If Machine 1 does total work in 24 days and machine B does the same in 30 days. Then the work can be 120 (LCM)
Machine A's rate- 10
Machine B's rate- 8

In one day, 3 shifts, they do a total work of = 27

Hence total number of days taken by them= 4.4

Bunuel . Can you help me with this?

Bunuel · Answer

Machine A can complete a certain job in 12 days, working 2 full shifts per day, which means in one shift A does 120/(12*2) = 5 units of work, not 10.

Machine B can complete the same job in 15 days, also working 2 full shifts per day, which means in one shift B does 120/(15*2) = 4 units of work, not 8.

In one day, they work 1.5 shifts each, hence do 7.5 and 6 units of work respectively.

120/(7.5 + 6) = 8.8...

Hope this helps.

DonBosco7 · Answer

Working 2 shifts machine A completes the job in 12 days.
Working 2 shifts machine B completes the job in 15 days.
SO if they work just one shift, that means they do only 1/2 the job.

Their original rate for completing 1 job.
A = 1/12
B = 1/15

Now, given that Machine A works during the first shift each day (only 1shift = 1/2 work), Machine B works during the second shift (only 1shift = 1/2 work), and both machines work half of the third shift (1/2 of a shift = 1/2 of 1/2 work = 1/4 work)

We need to find the time to complete the job --> T = W/R

1/2/12 + 1/2/15 + 1/4/12 +1/4/15 = 1/24 + 1/30 + 1/48 + 1/60 = 3/48 + 3/60 = 9/80

= 80/9 = 8.88 (approx. 9 days)

A furniture manufacturer has two machines, but only one can

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A furniture manufacturer has two machines, but only one can

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards