If Person A can do a job in 4 hours and Person B can do the same job in 2 hours...?

Question

...how long will it take them to do the job together??

Answer 1

Let t be the time for both to do the job together.
(1/4+1/2)t = 1
t = 4/3 hours

Answer 2

You need to qualify the type of work. Some work can not be done by two persons at the same time. They have to sit on each othere laps, or stand in the same hole digging dirt from under each otheres feet.

But if this does not apply as a rule Person A will start to tell jokes to person B slowwing this person down. Then they will start to argue about who will win the football game this week. Soon they start talking about co-workers , followed but ordering some carry out lunch and some beers. They figure out the boss is trying to cut one of their jobs so they both say
nuts to it, and spend the next 3 days proving the job should not be done in the first place.

The boss comes back and says this should have only taken you 2 hours. Because you cannot do this type of work any faster then the fastest person can do it. Input rate limit problem. He sits down and eats your pizza and drinks your beer explaining over the next 3 hours that certain work can not be done with mathmatical averaging, you are limited to the input limitations of the devices and requirements. Then you both have to listen to his vacation stories for another hour.

In the end both of you quit, by pushing the boss down the elevator shaft and following him.

2 hours...........


addition:
look I was having some fun but really you can not in many cases do the job any faster then the fastest person can do it. 2 hours. The other guy adds no value to the job it would take him 4 hours to do it. You cannot add or compound certian types of labor. Sad fact.

Answer 3

A - 1/4 of the job in 1 hour
B - 1/2 of the job in 1 hour

If they work together they can do 3/4 of the job in 1 hour.

They will require 4/3 hours or 1 hour and 20 minutes to complete the job together.

Answer 4

Easiest way to set up this problem is to think about what happens in 1 hour. Since it takes person A 4 hours to do the job, he can do 1/4 of it in one hour. Person B does 1/2 the job in one hour. Together it will take them an unknown amount of time (t) to do the job, so they will complete 1/t of the job in one hour.

So, in one hour

Person A's work + Person B's work = Together Work

1/4 + 1/2 = 1/t

to solve for t, we get a common denominator

t/4t + 2t/4t = 4/4t

(t + 2t)/4t = 4/4t

multiply by 4t on both sides.

t + 2t = 4

3t = 4
t = 4/3 hour.

Definitely check your answer on this problem.

in 4/3 hour A does 1/3 of the job
in 4/3 hour B does 2/3 of the job
Together, they complete the job.

Answer 5

1/4 = rate of A to do the job
1/2 = rate of B to do the job

1/4t + 1/2t = 1

(1 + 2)/4 t = 1
3/4t = 1
t = 4/3
t = 1.33 hours ==> time they will finish the job together

Answer 6

Take product over sum
4*2/(4+2) = 8/6 = 4/3 hours.
This is quickest way to get answer.

Answer 7

3 hours.