A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10

Question

A can do  \frac{1}{3}  of the work in 5 days and B can do  \frac{2}{5}  of the work in 10 days. In how many days both A and B together can do the work?

A) 7 \frac{3}{4}

B) 8 \frac{4}{5}

C) 9 \frac{3}{8}

D) 10

E) 12

generis · Answer

This approach looks time-consuming. It isn't. Find and add rates. Work is 1; flip the rate to get the number of days it would take A and B, working together, to finish.

RATES: To find rates, use   \frac{Work}{time} = rate

A's rate, in   \frac{Work}{days}  :
 \frac{(\frac{1}{3})}{5}=(\frac{1}{3} * \frac{1}{5})=\frac{1}{15}

B's rate:
 \frac{(\frac{2}{5})}{10}=(\frac{2}{5} * \frac{1}{10})=\frac{2}{50}=\frac{1}{25}

Add rates of A,  \frac{1}{15} , and B,  \frac{1}{25} , with LCM of 75. 
COMBINED RATE of A and B:

(\frac{5}{75} + \frac{3}{75}) = \frac{8}{75}

TIME: How many days does it take them, working together, to finish the job?
Job = 1
When work is 1, rate and time are inversely proportional.

Invert the combined rate,  \frac{8}{75} , to get the time:  \frac{75}{8} = 9\frac{3}{8}  days, OR

\frac{Work}{Rate} = time

\frac{1}{(\frac{8}{75})}= 1 * \frac{75}{8} =9\frac{3}{8}

Answer C

JeffTargetTestPrep · Answer

A’s rate is (1/3)/5 = 1/15 and B’s rate is (2/5)/10 = 2/50 = 1/25.

Their combined rate is 1/15 + 1/25 = 5/75 + 3/75 = 8/75.

Thus, the time it takes the two machines to complete the job is 1/(8/75) = 75/8 = 9 3/8 days.

Answer: C

CareerGeek · Answer

A can do  \frac{1}{3}  of the work in 5 days
--> A can do complete work in 3*5 days = 15

B can do  \frac{2}{5}  of the work in 10 days
--> B can do complete work in 10*5/2 days = 25

Assume work = LCM(15, 25) = 75 units
Formula: Work done = Rate of work x time
75 = Ra*15 and 75 = Rb*25
--> Rate of A = 5 units/day
--> Rate of B = 3 units/day

Both working together --> Total Rate = 5 + 3 = 8 units/day
--> 75 = 8*t
--> t = 75/8 = 9 \frac{3}{8}  days

IMO Option C

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Lampard42 · Answer

Rate of A= 1/(3*5)=1/15
Rate of B=2/(5*10)=1/25
So rate of A+B= 8/75 that is they require 75/8 days = 9 3/8 IMO C

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MathRevolution · Answer

A can-do  \frac{1}{3}  of the work in 5 days.

For 1 work, A will take 15 days.

In 1 day, A will complete  \frac{1}{15}  of the work.

B can do  \frac{2}{5}  of the work in 10 days.

For 1 work, B will take 25 days.

In 1 day, B will complete  \frac{1}{25}  of the work.

1 day work of (A + B ):  \frac{1}{15}  +  \frac{1}{25}  =  \frac{8}{75}

1 work will require  \frac{75}{8}  days or 9 \frac{3}{8}  days.

Answer C

DHRJ0032 · Answer

A's rate- 1/3 of work in 5 days.
so A can do the complete work in 15 days.
similarly B can do the whole work in 10x(5/2) i.e 25 days 
together they can do the work in xy/(x+y) days
i.e 25x15/(25+15) days i.e 75/8 days 
i.e 9 whole 3/8 days

ans: C

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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10

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