Really Easy Work/Rate problem

smclean23 wrote:Machine A working alone can complete a job in 3 1/2 hours. Machine B working alone can do the same job in 4 2/3 hours. How long will it take both machines working together at their respective constant rates to complete the job?

A) 1 hr 10 min

B) 2hr

C) 4hr 5 min

D) 7hr

E) 8 hr 10 min


OA is B......Please advise....

A's time = 7/2 , B's rate = 14/3

A's rate = 2/7, B's rate = 3/14

A's rate + B's rate = 2/7 + 3/14 = (4 + 3)/14 = 7/14 = 1/2

Hence A's time + B's time = 2/1 = 2 hrs

Hope this helps.

As you said, this is a really easy problem, as you do not need to solve it at all....

Just look at the answer choices, and there is only one option that can be the answer, and that is B....

machine A alone does the work in 3.5 hrs, so both machines working together cannot take more than 3.5 hrs....

that leaves us with only A and B

Now machine B takes more time than machine A to complete the same job...

Hence, answer HAS to be more than half of 3.5 hrs

Only possible answer is B, hence choose without calculation...

If you want to know the formula or working style for these kind of problems, it is like this....

Let the time taken for both of them to complete the work together be x.


Now, we know that

rate of work of A = 1/3.5 = 2/7

rate of work of b = 1/(14/3) = 3/14

now, when they work together,

rate X time = quantity of work

(2/7)x + (3/14)x = 1

solving, x = 2....

this would have taken you a little more than a minute, while the earlier solution would take you lesser than 20 secs...