Question

Jill and Sabrina can write a lab report together in $6$ hours. If all people work at the same rate, how many hours would it take to write a lab report if Kelly joins Jill and Sabrina?

Answer 1

Explanation:

Let jill, sabrina and kelly be x, y and z respectively.

xy = $6/hour

Assume x = y = z = c, that is they all work at the same rate.

Therefore, if x or y worked individually,

Rate of c = $6 × 2

= $12/hour

If kelly joins,

xyz = 3 × c

= $12/3

= $4/hour

Therefore if kelly joins, the rate will be $4/hour.

Answer 2

So if Jill, Sabrina and Kelly write the report together, it will take 4 hours.

Explanation:

We know that Jill and Sabrina can write a lab report together in 6 hours. We know that all people work at the same rate.

So, we conclude that it will take Jill or Sabrina 12 hours if they write the report themselves. Kelly will also need 12 hours to write a report because we know everyone is working at the same speed.

We conclude that if all three work together they will need three times less time. We get:

`x=(12)/(3)\\\\x=4`

So if Jill, Sabrina and Kelly write the report together, it will take 4 hours.