Machine P can produce x widgets in 10 hours, Machine Q can produce x

Question

Machine P can produce x widgets in 10 hours, Machine Q can produce x widgets in 6 hours, and Machine R can produce 2x widgets in 15 hours. If the three machines work together but independently, without interruption, how much time, expressed in hours, will be needed for them to produce 5x widgets?

A. 7 2/3
B. 8
C. 10 2/3
D. 12 1/2
E. 23 1/2

A. 7 2/3
B. 8
C. 10 2/3
D. 12 1/2
E. 23 1/2

Hatakekakashi · Answer

x in 10 hours i.e in 1 hour x/10
x in 6 hours i.e in 1 hour x/6 
x in 7.5 hours i.e in 1 hour x/7.5

widgets produced by machines combined in one hour = x/10 + x/6 + x/7.5 = 6+10+8/60 x = 24/60x = 2/5x

In one hour 2/5 x of widgets done

so in 5 hours 2x of widgets done

for 5x widgets 5x5/2 = 12 1/2

(D) imo

generis · Answer

Find combined rate (add rates), then divide work by rate to get time.
Rate of P:   \frac{x}{10}  
Rate of Q:   \frac{x}{6}  
Rate of R:   \frac{2x}{15}

All units are in hours. No need to write "units/hour." Time will be in hours.

Combined rate  
=   \frac{x}{10}+\frac{x}{6}+\frac{2x}{15}

Use LCM = 30
  \frac{x}{10}+\frac{x}{6}+\frac{2x}{15}

(\frac{3x}{30}+\frac{5x}{30}+\frac{4x}{30})=\frac{12x}{30}=\frac{6x}{15}=  Combined rate

Time needed to produce 5x widgets?

W= 5x ,  R*T = W , and  T= \frac{W}{R}

T =\frac{5x}{\frac{6x}{15}}=(5x*\frac{15}{6x})=\frac{75}{6}=\frac{25}{2}=12\frac{1}{2}   hrs

Answer D

pushpitkc · Answer

If machine P can produce x widgets in 10 hours, Machine Q can produce x widgets in 6 hours, and 
Machine R can produce 2x widgets in 15 hours, machine R can produce x widgets in  \frac{15}{2} = 7.5  hours.

Let's assume the total units of work(to produce x widgets) to be  30 units .
Now, machine P does the 3 units/hr, machine Q does 5 units/hr and machine R does 4 units/hr

Since we need to produce 5x widgets, the total units of work must be  150 units .
Together, they would do  3+5+4 = 12  units of work in an hour

Therefore, the three machines would take  \frac{150}{12} = 12\frac{1}{2}  hours to produce 5x widgets (Option D)

Mo2men · Answer

Time of machine P to produce = 10 hrs

Time of machine Q to produce = 6 hrs

Time of machine R to produce =  \frac{15}{2}  hrs...........Note: You will find later this easier than putting it 7.5 hrs

You can apply times fro above directly in this equation:

Total combined time =  \frac{P*Q*R}{(P*Q)+(P*R)+(R*Q)}

It may look intimidating but you will get directly combines time for x =  \frac{5}{2}

Time for 5x =  \frac{5*5}{2}  = 12.5

Answer: D

JeffTargetTestPrep · Answer

The combined rate of P, Q and R is:

x/10 + x/6 + 2x/15 = 3x/30 + 5x/30 + 4x/30 = 12x/30 = 2x/5.

We know that rate x time = total work. If we let t = the number of hours to produce 5x widgets, we can create the following equation;

(2x/5)(t) = 5x

2xt = 25x

2t = 25

t = 12.5

Answer: D

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Machine P can produce x widgets in 10 hours, Machine Q can produce x

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

Machine P can produce x widgets in 10 hours, Machine Q can produce x

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