# word problems

• Mar 20th 2009, 11:42 PM
princess_21
word problems
how to do this? i'm confused..

If A, B, and C work together in a job, it will take 1 1/3 hours. If only A and B work, it will take 1 5/7 hours. But if B and C work, it would take 2 2/5 hours. How long would it take each man working alone, to complete the job?

Thanks..
• Mar 21st 2009, 12:08 AM
u2_wa
Quote:

Originally Posted by princess_21
how to do this? i'm confused..

If A, B, and C work together in a job, it will take 1 1/3 hours. If only A and B work, it will take 1 5/7 hours. But if B and C work, it would take 2 2/5 hours. How long would it take each man working alone, to complete the job?

Thanks..

Time to complete the job by A: x hours
Time to complete the job by B: y hours
Time to complete the job by C: z hours

When all works together $\displaystyle T(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})=1$, where T=1 1/3 hours

When A and B works: $\displaystyle T'(\frac{1}{x}+\frac{1}{y})=1$, where T'=1 5/7 hours

When B and C works: $\displaystyle T''(\frac{1}{y}+\frac{1}{z})=1$, where T'' = 2 2/5 hours

Solve for x,y&z
Hope this helps
• Mar 21st 2009, 07:02 AM
stapel
Quote:

Originally Posted by princess_21
If A, B, and C work together in a job, it will take 1 1/3 hours. If only A and B work, it will take 1 5/7 hours. But if B and C work, it would take 2 2/5 hours. How long would it take each man working alone, to complete the job?

For "work" word problems, it's often best to start by converting the times to rates. For instance, if you can complete some task in three hours (the time), then you can do 1/3 of it each hour (the rate). If I take four hours to do the same thing, then I do only 1/4 of it each hour. If we worked together, we'd do 1/3 + 1/4 = 7/12 of it each hour.

. . . . .A's rate: 1/a
. . . . .B's rate: 1/b
. . . . .C's rate: 1/c

You are given that the time for A & B together is 12/7 hours, the time for B & C together is 12/5 hours, and the time for all three together is 4/3 hours. Then:

. . . . .A & B together: 1/a + 1/b = 7/12
. . . . .B & C together: 1/b + 1/c = 5/12
. . . . .all three together: 1/a + 1/b + 1/c = 3/4

This gives you three rational equations in three unknowns (ouch!). I'd start by subtracting the first line above from the third, giving us:

. . . . .$\displaystyle \frac{1}{c}\, =\, \frac{2}{12}\, =\, \frac{1}{6}$

Solve this for the value of "c". Then subtract the second line from the third line, and solve the result for the value of "a". Plug this value into the first equation, and back-solve for the value of "b".

• Mar 30th 2009, 03:17 AM
princess_21
Quote:

Originally Posted by stapel
For "work" word problems, it's often best to start by converting the times to rates. For instance, if you can complete some task in three hours (the time), then you can do 1/3 of it each hour (the rate). If I take four hours to do the same thing, then I do only 1/4 of it each hour. If we worked together, we'd do 1/3 + 1/4 = 7/12 of it each hour.

. . . . .A's rate: 1/a
. . . . .B's rate: 1/b
. . . . .C's rate: 1/c

You are given that the time for A & B together is 12/7 hours, the time for B & C together is 12/5 hours, and the time for all three together is 4/3 hours. Then:

. . . . .A & B together: 1/a + 1/b = 7/12
. . . . .B & C together: 1/b + 1/c = 5/12
. . . . .all three together: 1/a + 1/b + 1/c = 3/4

This gives you three rational equations in three unknowns (ouch!). I'd start by subtracting the first line above from the third, giving us:

. . . . .$\displaystyle \frac{1}{c}\, =\, \frac{2}{12}\, =\, \frac{1}{6}$

Solve this for the value of "c". Then subtract the second line from the third line, and solve the result for the value of "a". Plug this value into the first equation, and back-solve for the value of "b".

.$\displaystyle \frac{1}{c}\, =\, \frac{2}{12}\, =\, \frac{1}{6}$

i think i'm getting to the answer.
thank you very much
• Mar 30th 2009, 05:16 AM
princess_21
1/A + 1/B + 1/C= 3/4
1/A + 1/B= 7/12
1/B + 1/C= 5/12

1/A=1/3
1/B=1/4
1/C=1/6

then
A= 3 hrs.
B=4 hrs.
C=6 hrs.