another wonderful word problem

[Kimbers0812]

I am doing a practice final and totally lost on these word problems....need help before tomorrow if anybody can help me...

If A can do a job in 104 hours and it takes A and B working together 40 hours to do the same job, how long will it take B working alone to do the same job?

Thanks again!

 

[Mrspi]

I am doing a practice final and totally lost on these word problems....need help before tomorrow if anybody can help me...

If A can do a job in 104 hours and it takes A and B working together 40 hours to do the same job, how long will it take B working alone to do the same job?

Thanks again!

Let x = number of hours for B to do the job alone. In 1 hour, B does 1/x of the job, and in 40 hours, B does 40 / x of the job.

A can do the job alone in 104 hours, so in one hour A does 1/104 of the job, and in 40 hours A does 40/104 of the job.

If A and B work together, then

part of job done by A + part of job done by B = whole job
40 / 104 + 40 / x = 1

Solve that for x.....

 

[TchrWill]

<< If it takes me 2 hours to paint a room and you 3 hours, ow long will it take to paint it together? >>

Method 1:

1--A can paint the house in 5 hours.
2--B can paint the house in 3 hours.
3--A's rate of painting is 1 house per A hours (5 hours) or 1/A (1/5) houses/hour.
4--B's rate of painting is 1 house per B hours (3 hours) or 1/B (1/3) houses/hour.
5--Their combined rate of painting is 1/A + 1/B (1/5 + 1/3) = (A+B)/AB (8/15) houses /hour.
6--Therefore, the time required for both of them to paint the 1 house is 1 house/(A+B)/AB houses/hour = AB/(A+B) = 5(3)/(5+3) = 15/8 hours = 1 hour-52.5 minutes.

Note - T = AB/(A + B), where AB/(A + B) is one half the harmonic mean of the individual times, A and B.

Method 2:

Consider the following diagram -

.........._______________ _________________
..........I B /............................/\
..........I..*.................../..............................I
..........I.....*............../................................I
..........Iy.......*........./.................................I
..........I................./...................................{
..........I*****x****** ....................................{
..........I............./....*................................(c)
..........I(c-y)..../.........*...............................{
..........I......../...............*...........................I.
..........I....../....................*........................I
..........I..../.........................*.....................I
..........I../.............................*...................{
.........I./___________________* ________\/__
A

1--Let c represent the area of the house to be painted.
2--Let A = the number of hours it takes A to paint the house.
3--Let B = the number of hours it takes B to paint the house.
4--A and B start painting at the same point but proceed in opposite directions around the house.
5--Eventually they meet in x hours, each having painted an area proportional to their individual painting rates.
6--A will have painted y square feet and B will have painted (c-y) square feet.
7--From the figure, A/c = x/y or Ay = cx.
8--Similarly, B/c = x/(c-y) or by = bc - cx.
9--From 7 & 8, y = cx/a = (bc - cx)/b from which x = AB/(A+B), one half of the harmonic mean of A and B.

You now have the tool to solve your own problem since you have T and A and need only solve for B.

I think this should give you enough of a clue as to how to solve your particular problem.