Person A completes the job in Hours
Person B completes the job in Hours

If it takes Person A 7 hours to do something

and Person B, 6 hours to do something

how long would it take if they worked together?

##### Use Work Formula:

1/r + 1/s = 1/t

This means the inverse of time it would take everyone working together equals

the sum of the inverses of times it would take each person working individually

##### Given r = 7 and s = 6, we have:

 1 7
 +
 1 6

The denominators of our 2 fractions are not equal.
We need to have matching denominators in order to add the 2 fractions.

To do this, we multiply the numerator of fraction 1 by the denominator of fraction 2.
We also multiply the numerator of fraction 2 by the denominator
of fraction 1 as illustrated below.

##### Denominator

We add those 2 results, and get our numerator. Our denominator is the product of the denominators of both fractions.

 Fraction 1 + Fraction 2  = Numerator 1 x Denominator 2 + Numerator 2 x Denominator 1 Denominator 1 x Denominator 2

 Fraction 1 + Fraction 2  = 1 x 6 + 1 x 7 7 x 6

 Fraction 1 + Fraction 2  = 6 + 7 42

 Fraction 1 + Fraction 2  = 13 42

##### Solve for t:

 1 t
 =
 13 42

 t  = 42 13

##### Convert to minutes:

 Minutes  = 60 x 42 13

 Minutes  = 2520 13

In minutes, this is equal to 193.84615384615

In hours, this is equal to 3 hours, 13 minutes also equal to 3.2307692307692 hours

##### What is the Answer?
In hours, this is equal to 3 hours, 13 minutes also equal to 3.2307692307692 hours
##### How does the Work Word Problems Calculator work?
Free Work Word Problems Calculator - Given Person or Object A doing a job in (r) units of time and Person or Object B doing a job in (s) units of time, this calculates how long it would take if they combined to do the job.
This calculator has 2 inputs.

### What 1 formula is used for the Work Word Problems Calculator?

1/r + 1/s = 1/t

For more math formulas, check out our Formula Dossier

### What 3 concepts are covered in the Work Word Problems Calculator?

word problem
Math problems involving a lengthy description and not just math symbols
work
Measure of energy transfer when an object moves
W = F * d
work word problems