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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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Intern
Joined: 25 Jun 2014
Posts: 42
GMAT 1: 690 Q48 V37
WE: Operations (Computer Software)
A is 1.5 times as fast as B. A alone can do the work in 20 days. If A  [#permalink]

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19 Feb 2016, 22:22
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Difficulty:

35% (medium)

Question Stats:

75% (02:21) correct 25% (02:09) wrong based on 121 sessions

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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

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Joined: 18 Sep 2014
Posts: 228
Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A  [#permalink]

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19 Feb 2016, 23:14
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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)

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Joined: 17 Feb 2016
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A is 1.5 times as fast as B. A alone can do the work in 20 days. If A  [#permalink]

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21 Feb 2016, 00:09
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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

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Joined: 25 Sep 2015
Posts: 107
Location: United States
GMAT 1: 700 Q48 V37
GPA: 3.26
Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A  [#permalink]

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25 Feb 2016, 16:28
Mesto wrote:
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

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
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Joined: 17 Jul 2014
Posts: 2598
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A  [#permalink]

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04 May 2016, 18:46
1
Mesto wrote:
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

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.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India
Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A  [#permalink]

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04 May 2016, 19:49
Mesto wrote:
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

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.

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Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 14 Mar 2017
Posts: 5
Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A  [#permalink]

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25 Apr 2017, 05:44
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
Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A &nbs [#permalink] 25 Apr 2017, 05:44
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