Working individually, Jake, John, and Jordyn can do a job in

Question

Working individually, Jake, John, and Jordyn can do a job in 16, 48, and 96 hours, respectively. It was decided that they would take turns working on the job successively for an hour. Anyone can start the work, and others will follow.

Select in the table the    Maximum    hours and    Minimum    hours required to complete the job.

Make only two selections, one in each column.

HarshaBujji · Answer

Let's assume there are 96 units of work. (96 is the LCM of 16,48,96).

So in 1 hour 
Jake can do : 6 units 
John can do : 2 units
Jordan can do : 1 unit.

So 9 units of work in 3 hrs. But we don't know who started first.

So till 90 units of work no issue BCS every one will work 10 hrs each. So the remaining 6 units are pending.

Minimum Condition : Jake starts so after 30 hrs Jake gets a chance. 30+1 hr : 31hrs. 
 Maximum Condition:  Jordan starts followed by John: 1hr Jordan completes 1 unit, Remaining 5 units John completes 2 units in next hr, Finally 3 units is left which will be done by Jake in 30m.

So total time 30+1+1+0.5 =32.5.

nafuzzz · Answer

Maximum: 32.5
Minimum: 31

a bit challenging but fun

Bismuth83 · Answer

1. Let there be W work. Jake, John, and Jordyn work at speeds  \frac{W}{16} ,  \frac{W}{48} , and  \frac{W}{96} , respectively.

2. The key thing to notice is that for every 3 hours, each person must've worked exactly 1 hour. During that time  \frac{W}{16} + \frac{W}{48} + \frac{W}{96} = \frac{6W + 2W + W}{96} = \frac{3W}{32}  work was done.

3. After 30 hours  \frac{3W}{32} * 10 = \frac{30W}{32}  work was done and  W - \frac{30W}{32} = \frac{2W}{32} = \frac{W}{16}  work is left.

4. Since  \frac{W}{16}  is less than  \frac{3W}{32} , the time that will be needed to do the work depends on the order of the workers.

5. The job will take the minimum amount of time if we choose the faster workers first. It will take 1 extra hour for Jake to make a total of 31.

6. Likewise, the job will take the maximum amount of time if we choose the slower workers first. It will take  2 + \frac{\frac{W}{16} - \frac{W}{48} * 1 - \frac{W}{96} * 1}{\frac{W}{16}} = 2 + (1 - \frac{\frac{3}{96}}{\frac{1}{16}}) = 2 + (1 - 0.5) = 2.5  extra hours with Jordyn, then John, and then Jake working to make a total of 32.5.

7. Our answer will be:   Maximum Hours - 32.5 and Minimum Hours - 31  .

Working individually, Jake, John, and Jordyn can do a job in

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 Two-part Analysis (TPA) Questions

Working individually, Jake, John, and Jordyn can do a job in

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