Math question

Question

Computer A can do a job in4 hours. Computer B can do the same job in2 hours. How long will it take them working together?

Answer 1

Let's mark the job, which has to be done as "1", then productivity of computer A is 1/4 and productivity of computer B is 1/2. If both computer will do the same job together their joint productivity will be the sum of their individual productivity:
1/4 + 1/2 = 3/4
Thus, two computer can do 3 similar jobs in 4 hours, then 1 job they will do in 4/3 = 1 hour 20 minutes.

Answer 2

Hello again, T -- we know the combined effort will take less than 2 hours, since A is helping B ... if A were as fast as B, then the job would take 1hr or half the time ... STAIR-STEP: 1hr, 1/2B + 1/4A ... leaves 1/4 job to finish, which is 1/3 more to do ... go another 20min, 1/2 + 1/6B and 1/4 + 1/12A = 6+2+3+1 twelvths => 1hr 20min :)

Answer 3

all correct ansers BUT IMNSHO the most efficient way to solve a problem like this is:

 

PRODUCT/SUM

 

i.e . in this example

 

4 X 2/4+2= 8/6= 1 1/3 hrs or 1 hr 20 minutes

 

Jim Coleman

Answer 4

Think of it like this. Let J or 1J represent the completed job. Then, for the first computer, in every hour it completes J/4 of the job, since it takes 4 hours to complete the job. Similarly, for the second computer, in every hour it completes J/2 of the job, since it takes 2 hours to complete the job. Now, with both computers, working simultaneously, (J/4+J/2) of the jobdone being done every hour. That is, (J/4+2J/4 = 3J/4) of the job is being done every hour. We have this relationship.    (3/4)J ___relates to ____1 hours. That is, 1J ___relates to .... You can complete this. This pattern of reasoning can be used to solve any such "work problem". 

Answer 5

Hello Titaree,

We can generalize this question a bit, so that you can have a formula for similar problems at hand.

Suppose Computer A (or Machine A, Person A, etc.) can do 1 job in x hours, and Computer B can do 1 job in y hours.  These are equivalent to

Computer A:     (1/x) job in 1 hour

Computer B:     (1/y) job in 1 hour

since we make the assumption that these computers work at the same pace throughout the job.

Then, in 1 hour, Computer A and Computer B working together will finish the sum of the portions of a job that each completes on its own, namely:

Computer A and Computer B together:  ((1/x) + (1/y)) job in 1 hour  =>  (x+y)/(xy) job in 1 hour.

Now, we are interested in how long it takes to complete one job, so if we "multiply through" the last statement by the reciprocal of (x+y)/(xy), we get:

A and B together:   1 job in (xy)/(x+y) hours.

At this point, you may substitute the quantities for x and y from your problem to find the solution. 

Note that you may generalize this technique further in several directions, but the principle is the same.

Regards,

Hassan H.