Given amount of work = 100 If A alone does the work, it

Question

Given amount of work = 100

If A alone does the work, it takes 5 hours.

If A and B do the work together, it takes 2 hours.

If B alone does the work, how long will it take?

ywilfred · Answer

A - 100 work in 5 hours -> 20 work in 1 hour
A & B - 100 work in 2 hours -> 50 work in 1 hour

So in 1 hour, B does 30 work. So 100 work takes 100/30 = 3.3 hours.

Titleist · Answer

A does 20 units of work per hour 

B must do 30 units per hour

Together they complete 100 work units in 2 hours

Thus 100units/30units/hour = 3 1/3 hours

GMATT73 · Answer

Alternative time saving method (regardless of work volume)

Work Rate Formula: AB/A+B= Total Job Time

5B/5+B=2 ---> 5B=10+2B --->3B=10 ---> B=3.33hrs (3 hrs 20 minutes)

cool_jonny009 · Answer

A=5

together (A*B)/(A+B) = 2 

5B = 2(5+B)= 10+2B


B = 10/3=3.33

Jennif102 · Answer

let me share w/ you one of the best tricks i've learned for Gmat problems so far....anytime you have a work problem like this always take the # of hours per person and make it a fraction w/ the hours in the denominator and 1 in the numerator. Add them all together (must get a common denominator of course). Then flip the total around and that's the total time it takes!

Here's how I solved this one:

we know it takes A 5 hours alone.
so....1/a =--> 1/5=20/100 (because if you flip the answer- 100 goes into 20 5 times, which is A's total time)
so 1/A + 1/B = 2 hours, which would be 50/100

so...1/5 + 1/B = 50/100
common denominator: 20/100 + 1/b = 50/100

We can easily see that B must equal 30.
Flip 30/100 around and you get 3 1/3

gamjatang · Answer

GMATT73 provided a nice tip :  it's regardless of work volume (=100) 

Here's the shortest way (as is explained by Gmatt73)

1/a = 1/5
1/a + 1/b = 1/2

hence, 1/b = 3/10 and b = 10/3

rahulraao · Answer

My way of doing this - 

If A does it in ta hours
If B does it in tb hours
If time together is T hours

Then, T = (ta x tb)/(ta + tb)
Similarly, 

If we are given the T and ta and we are to find out tb, then

tb = (ta-T)/(T x ta) hours.

So here, tb = (5-2)/(5x2) = 3.3 hours.

Given amount of work = 100 If A alone does the work, it

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