Question

Tiana can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. If they decide to clear the field together, how long will it take them?

Answer 1

For this case, the first thing we must do is define a variable.

We have then:

t: time it will take Tiana and Jacob to finish the work together.

We have then that the equation that models the problem is given by:

$\frac{1}{3} + \frac{1}{2} = \frac{1}{t}$

From here, we clear the value of t.

For this, we follow the following steps:

1) Multiply both sides of the equation by 6t:

$\frac{6t}{3} + \frac{6t}{2} = \frac{6t}{t}$

2) Simplify both sides of the equation:

$2t + 3t = 6$

3) Add similar terms:

$5t = 6$

4) Clear the value of t.

$t = \frac{6}{5}$

Answer:

If they decide to clear the field together they will take them about 6/5 hours

Answer 2

Let us determine each of their rates of work:

Since Tiana can clear the field in 3 hours, meaning she can do 1/3 of the work per hour.

In the same way, Jacob can do 1/2 of the work per hour. 

Now, what would be the rate of work if they were working together? Let's look at it like this:

Hours to complete the job:
Tiana = 3
Jacob = 2
Together = t

Work done per hour:
Tiana = 1/3
Jacob = 1/2
Together = 1/t

If you add their labor together:

1/3 + 1/2 = 1/t
5/6 = 1/t
t = 6/2 = 1.2

Together, they can clear the field in 1.2 hours.