It takes 12 hours for Adam to paint a certain wall ; 8 hours for Ben .

Question

(Work rate) It takes 12 hours for Adam to paint a certain wall, and 8 hours for Ben to paint the same wall. Adam painted alone for 3 hours, and then Ben came to help Adam paint. After a while, Adam left, and Ben finished the job on his own in 1 hour. How many hours did Adam and Ben work together?

A. 1
B. 3
C. 5
D. 7
E. 9

A. 1 
B. 3 
C. 5 
D. 7 
E. 9

yashikaaggarwal · Accepted Answer

Let the total work be 24 ( LCM of 12&8) 
So Adam does 24 work in 12 hours (2 work/hour) 
And Ben does 24 work in 8 hours (3 work/hour)

Adam started work and did work all alone for 3 hours. 
3hours*2work = 6 work. ------------(1)

Ben joins in 4th hour. And they do work together. Adam+Ben = 2+3 = 5work/hour ------------(2)

And after some time Adam left leaving 1 hour work behind for Ben to complete. 
Ben do 3 work per hour. 
So Ben did 3 work in last hour -----------(3)

Work done in first 3 hours = 6
Work done in last hour = 3
Work left to be done in between= 24-6-3 = 15 work

They both did 15 work in 15/5 = 3 hours

Answer is B

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Archit3110 · Answer

given rate of A ; 1/12 and B 1/8
so in 3 hours A did 3x/12 ; x/4 work
left with 3x/4
which is done in two parts
part 1 ; B + A work together for n hours ; n*(1/12+1/8) ; n* 5/24
part 2 ; B works for 1 hour ; 1/8
we get
5n/24 + 1/8 = 3x/4
let x = 1
5n+3 = 3*24/4
solve for n 
5n= 15 ; n = 3
OPTION B

kiranbhasker · Answer

Let total amount of work be LCM of 12,8 = 24

Adam does 24 units of work in 12 hours, rate is 2 units/hour
Ben does 24 units of work alone in 8 hours, rate is 3 units/hour.

Adam works alone for 3 hours initially,
hence 24- 3(2) = 18
Ben works alone for 1 hour , 18-1(3) = 15.
since they have completed the work the duration of work done by both together = 15/3+2 =  3 hours.

MathRevolution · Answer

(Solution):

Adam takes 12 hours to paint a certain wall. In 1 hour, Adam will paint  \frac{1}{12}  of the wall.

Ben takes 8 hours to paint a certain wall. In 1 hour, Adam will paint  \frac{1}{8}  of the wall.

Adam started work and painted alone for 3 hours. Therefore, the amount of work done by Adam is:

=>  \frac{1}{12}  * 3 =  \frac{1}{4} .

Adam and Ben together can finish ( \frac{1}{12}  +  \frac{1}{8}  =  \frac{5}{24} ) work in 1 hour.

Ben painted for 1 hour alone at the end. Therefore, the amount of work done by Ben is:

=> 1 *  \frac{1}{8}  =  \frac{1}{8} .

Total work done:

=>  \frac{1}{4}  +  \frac{1}{8}  =  \frac{3}{8} .

Remaining work:

=> 1 -  \frac{3}{8}  =  \frac{5}{8}  of the work.

This work was done by Adam and Ben together:

=>  \frac{5}{24}  work in 1 hour =  \frac{5}{8}  the part of work to be completed in 3 hours since ( \frac{5}{24} ) * 3 =  \frac{5}{8} .

Hence, Adam and Ben worked together for 3 hours.

Therefore, B is the correct answer

Answer B

bumpbot · Answer

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It takes 12 hours for Adam to paint a certain wall ; 8 hours for Ben .

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It takes 12 hours for Adam to paint a certain wall ; 8 hours for Ben .

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