A is 1.5 times as fast as B. A alone can do the work in 20 days. If A

Question

A is 1.5 times as fast as B. A alone can do the work in 20 days. If A and B work on alternative days, beginning with A, in how many days will the work be completed?

A) 23
B) 22
C) 21
D) 24
E) 25

FightToSurvive · Accepted Answer

A can do the work in 20 days = 100/20 =5% of the work can be completed in 1 day by A
B can do the work in 1.5*20 = 30 days (100/30) =3.33% of the work can be completed in 1 day by B.
Starting alternatively from A and B (Combined work = 5+3.33 = 8.33%) of the work can be completed in  2 days .
Therefore, 100/8.33 = 12 (which means 12*2 = 24 days)

Hence D is the answer.

sydneygmat1 · Answer

A can finish 1 work in 20 days 
B can finish 1/1.5 work in 20 days - since A is 1.5 faster than B

This means 
B can finish 1 work in 20*1.5 days = 30 days

Now using the awesome GMAT formula when two machines work together they can finish the job in = AB/ (A+B) = 20*30/(20+30) = 20*30/50 = 12 days

Since they alternate on days, it will take them double this time so total time = 12 * 2 = 24 days

So answer is D

rsh12 · Answer

Time taken by A - 20 days
A - Rate = 1/20 to complete 1 job.

B rate is 1/(20*1.5) = 1/30

Total number of days taken by both of them together working alternatively= X

Work-Time equation
X/(2*20) + X/(2*30) = 1

Solving, X=24

mvictor · Answer

1/20 = 1/A
1/A = 1.5/B
B must be 1/30

i found it easy to set a task consisting of 60 units.
A does 3 units per day, B does 2 units per day. in 2 days, A and B get done 5 units of work. since we need a 60/5 = 12 series of alternative days, the task will be completed in 12*2=24 days.

KarishmaB · Answer

Using ratios can help too.
Ratio of speed = 1.5:1= 3:2
Ratio of time taken = 2:3 
So B alone takes 30 days
Together, working alternate days, the two of them complete 1/20 + 1/30 = 5/60 of the work every 2 days.
So they take (60/5 = 12)*2 = 24 days to complete the work.

Answer (D)

ppcm · Answer

A's rate = 1/20
B's rate = 1/(20*1.5) = 1/30
The alternative time is the double of the time for A & B together
(1/20 + 1/30) * (1/2 T) = 1
T/20 = 6/5
T=24

Archit3110 · Answer

time taken by A ; 20 days
time of B would be 20*1.5 ; 30 days
working together combined rate ; 1/20+1/30 ; 5/60 ; 1/12 or say 12
alternate working hence total time ; 2*12 ; 24 days
OPTION D

ThatDudeKnows · Answer

I don't like fractional rates, so let's make up a number that makes sense for the job. How about defining the job as solving 60 GMAT questions. A can do it in 20 days, so A solves 3 per day. A is 1.5 times as fast as B, so B solves 2 per day.

Working on alternating days, they will solve 5 questions every 2 days. We need 12*5questions, so it's going to take 12*2days = 24.

Answer choice D.

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A is 1.5 times as fast as B. A alone can do the work in 20 days. If A

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A is 1.5 times as fast as B. A alone can do the work in 20 days. If A

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