Can you please help me with this?

Question

Bob and Alice can finish a job together in three hours. If Bob can do the job by himself in five hours, what percent of the job does Alice do?

(A) 20% (B) 30% (C) 40% (D) 50% (E) 60%

Answer 1

Hello, Sona,

Let's try to solve this with a couple of equations. We have two workers with 2 different rates of "doing a job." While it might seem it is hard to establish a rate, such as 5 bikes/day, we can still use the relationships.

Set Bob's rate to B (we'll say B has the unit hours/job)

Set Alice's rate to A

We know that at three hours Bob and Alice complete one job (J).

This can be made into an equation:

3*(B + A) = J : Bob and Alice working at their own rates can complete one Job in 3 hours.

We can also use Bob's information:

5B = J : Bob can complete the same Job in 5 hours

Well, look at what we have: two equations that are both equal to 1J. Let's use Bob's information for J, and substitute it into the first equation:

3B +3A = 5B

2B = 3A

Bob's rate is 2/3 Alice's rate. (I know what you are thinking - that's high for a man).

Let's say the rates are Jobs/hour (it can be anything), just so we can visualize what this equations is saying. In 1 hour, Bob makes 2 units and Alice makes 3. Hmmmm, . . . that's 5 units total. The percentage that Alice does is

3/5, or 60%

I hope this helps,

Bob

Answer 2

In I hour bob does 1/5 of the job

In 1 hour Alice does 1/a of the job

Together they do 1/3 of the job in an hour

So 1/5 + 1/a = 1/3

1/a = 1/3 - 1/5

1/a = 5/15 -3/15 = 2/15

a= 15/2= 7 1/2 hours