Expert: Pawan Musale - 8/14/2009

Question
If Thumbelina's team can build a prefabricated home in 15 hours and Rumplestillskin's team takes 10 hours to do the same job, how long will it take both teams, working together, to complete the job?



I want to also know if this problem has enough information.. I don't think it does.

Answer
Maria,

This problem has sufficient information. We will solve this.

Let us denote Thumbelina's team with T and Rumplestillskin's team with R.

Now, T can build 1 home in 15 hrs.
So write this in following manner:

                 Work (Home)          Time (hr)
                      1                15
                      x                 1

x is the amount of work that T can build in one hour.

In such case, to find x, cross multiply the terms and equate the results like:

1 * 1 = x * 15

Solving this,

x=1/15 --------------------------------------------------------- #1

Means T can build 1/15 home in 1 hr.

Let us repeat the same thing for R.

Now, R can build 1 home in 10 hrs.
So write this in following manner:

                 Work (Home)          Time (hr)
                      1                10
                      y                 1

y is the amount of work that R can build in one hour.

In such case, to find y, cross multiply the terms and equate the results like:

1 * 1 = y * 10

Solving this,

y=1/10 ---------------------------------------------------------- #2

Means R can build 1/10 home in 1 hr.

Now if both the teams start together, then they collectively can build (x+y) home in 1 hr.

So they will build 1/15 + 1/10 home in one hr.

1/15 + 1/10 = 1/6

So they together will build 1/6 home in 1 hr. Again write this in the table format as:

                   Work (Home)          Time (hr)
                      1/6               1
                      1                 z

Means, to build 1/6 home, team needs 1 hr, so to build 1 home, team will need z hrs.

Cross multiplying,

1/6 * z = 1 * 1
Solving,

z=6

So if both teams start together, they will complete the home in 6 hrs.

I hope this solves your question.

Kindly let me know if you need additional information.

All the best. :)

Regards,
Pawan