work rate

mariah wrote:Person A completed 1/4 of a certain work in two hours. Then A and B completed the remaining work in 4.5 hours. How long time will it take for B to complete the work independently?

oa is 16 but i think it not right

If A alone does 1/4 of the job in 2 hours, then A will do 1 job in 8 hours for a rate of 1/8.

If A + B do 3/4 of the job in 4.5 hours, then together they will do 1 job in 6 hours for a rate of 1/6.

A + B = A + B

1/8 + B = 1/6

B = 1/6 - 1/8

B = 8/48 - 6/48 = 2/48 = 1/12
B can do 1 job alone in 24 hours.

-Carrie

mariah wrote:A and B need two hours to produce 3000 products. If B works at half of its rate, they need three hours to finish the same work. What A's rate?

A+B = 3000/2 = 1500 per hour

A + B/2 = 3000/3 = 1000 per hour

Here are two ways to solve it.

If A + B/2 is 500 less than A + B, then B must be making 500 less products per hour at half his rate, so B normally makes 2*500 = 1000 product per hour.

Then A + 1000 = 1500
A = 500

OR

A + B = 1500

A + B/2 = 1000
multiply both sides by 2 to get 2A+B = 2000

Now just line up the equations and subtract:
2A + B = 2000
-A + B = 1500
------------------
A = 500

So As rate is 500 per hour.

-Carrie

daim official answer is wrong !! it is 24 hrs not 16!!


mistake is probably in the wording we are not interpreting it right

1 oa must be 18
...to complete the job

2 getting 500 as well

mariah wrote:1 oa must be 18
...to complete the job

Wow, that wording is open to interpretation. I read it as "complete the entire job on his own," which would be the rate for 1 job, which is 24 hours.

But I can see (maybe) how it can be read as "complete the 3/4 of the job that A+B did together," which would be 3/4 of 24 hours = 18.

Where did the question come from?

-Carrie

from unoficial source