rates/widget problem with sharing - please help!!

Question

Mike and David are each assigned to produce x identical widgets. Based on their respective rates, Dave calculates that it will take him 5 hours to produce the widgets while Mike calculates that it will take him 2 hours longer than Dave. Dave agrees to make Y of Mikes widgets so that they can each complete the task in the same amount of time. What is the number of widgets, interms of y, that Mike was assigned to make?

Please help!!

Please help!!

mikemcgarry · Answer

Dear clearmountain , First of all, I love your screenname. :-)

You may find this blog article helpful: https://magoosh.com/gmat/2012/gmat-work-rate-questions/ Here: each is assigned x widgets to make, and Dave takes y away from Mike's load, so Dave makes x + y and Mike must make x - y. (amount) = (rate)(time) ====> A = RT Dave's rate = amount/time = x/5 Mike's rate = x/7 For Dave: A = RT ---> x+y = (x/5)*T ---> 5(x+y)/x = T For Mike: A = RT ---> x-y = (x/7)*T ---> 7(x-y)/x = T Both T's are equal, so set these equations equal: 5(x+y)/x = 7(x-y)/x ---- then multiply by x ---> 5(x+y) = 7(x-y) ---- then distribute ---> 5x + 5y = 7x - 7y --- then combine terms ---> 12y = 2x We want to solve for " the number of widgets ... that Mike was assigned to make " = x, in terms of y. Divide by 2. 6y = x So, the number of widgets each was assigned to make, x, is equal to 6y. Does that make sense? Mike :-)

clearmountain · Answer

Thanks Mike. Perfect sense. Andrew

clearmountain · Answer

can you do it with a plug in method? thanks.

mikemcgarry · Answer

Andrew Hmmm. I don't know if that would be much simpler. We need this in terms of y, so we can't really pick a number for y. If we pick a number for x and not for y, the solution is going to be almost identical. If this were a full GMAT problem, with five answer choices in terms of y, then we could pick numbers for x and y, calculate the numerical answer, and plug those same values into the answer choices to see which one matched. If this is a genuine GMAT problem with answer choices, and you provide those answer choices, I can show that numerical approach. In the meantime, you may find the following post helpful. https://magoosh.com/gmat/2012/variables- ... -approach/ Mike :-)

KarishmaB · Answer

Another method that uses fewer variables but needs you to understand the question well:

Dave completes 1 work (i.e. making x widgets) in 5 hrs. Rate of work = 1/5 work/hr
Mike completes 1 work in 7 hrs. Rate of work = 1/7 work/hr

They work for the same amount of time and complete 2 work together. Combined rate of work: 1/5 + 1/7 = 12/35
Time for which each person works = Work/Rate = 2/(12/35) = 35/6 hrs

So, Dave works for a total of 35/6 hrs. He takes 5 hrs to complete his own work and uses rest of the (35/6 - 5) = 5/6 hrs to make y widgets for Mike.
Dave takes 5 hrs to make x widgets and 5/6 hrs to make y widgets hence, y = (1/6)x or x = 6y

madhavgmat · Answer

Hi Karishma

couldnt understand the last line..
Dave takes 5 hrs to make x widgets and 5/6 hrs to make y widgets hence, y = (1/6)x or x = 6y ...

can you explain how you got y = (1/6)x

ShalabhsQuants · Answer

Another way to look at this problem without considering variable is to assume that there are 35 (Instead of X) widgets to be completed by each.

Why 35??( B'coz 35 being LCM of 5, & 7; 35 will be easily divisible by both 5, & 7)

It means Dave's rate is 7 widgets/hr.(35/7), while Mike's rate is 5 widgets/hr.(35/7).

In 5 hrs. Dave will finish his total 35 widgets, while Mike will be left with 10 more widgets to be completed. (He will complete only 25 widgets).

These remaining 10 widgets will be completed by Dave, & mike together.

As Dave's speed is more than Mike, hence remaining 10 widgets load will be distributed in the ratio of 1/5:1/7. This will yield Dave's additional widgets load equals 10*(7/12) = 70/12. In question variable terms, it is y.

As stated here X= 35, & Y is 70/12. So X/Y = 35/(70/12) = 6, or X = 6Y.

KarishmaB · Answer

Say, a machine takes 2 hrs to make 100 widgets one after another (not parallel work). How many will it make in 1 hr? I am sure you will say 50 widgets.
Now think, a machine takes 2 hrs to make x widgets. It takes 1 hr to make y widgets. Can I say x = 2y? Sure! x must be double of y.
Similarly, if x widgets are made in 5 hrs and y are made in 5/6 hrs, y must be 1/6 of x. Therefore, y = x/6 or x = 6y.

madhavgmat · Answer

Thanks a lot karishma for your explanation.....really upset with myself that simple things don't get into my head sometimes.

By the way, I did like ShalabhsQuants method (plugging values) to solve this problem.

rates/widget problem with sharing - please help!!

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