I raked leaves for six hours, John raked leaves in seven hours. How long would it take if we worked together?

Let's set up an equation for this problem.

If one person can rake leaves in 6 hours, that means they can do 1/6 of the job in 1 hour.

If one person can rake leaves in 7 hours, that means they can do 1/7 of the job in 1 hour.

We want to determine the time it would take them to do it together, which is our unknown. We will call our unknown** t. (t = time)**

Therefore our equation will be 1/6t + 1/7t = 1/t.

We will find the least common denominator which will be **42t.**

We will multiply both sides of the equation by the least common denominator** 42t.**

**42t** (1/6t) + **42t** (1/7t) = **42t** (1/t)

= 7t + 6t = 42

=13t = 42

We will divide both sides by 13 **(Division is the inverse operation of multiplication)**

**
**13t/

**13**= 42/

**13**

**t= 3.230769 which we will round to 3.23 **

**It will take them both 3 23/100 hours to do it together.**

To convert 23/100 into minutes we will use a proportion.

We know there are 60 minutes in an hour so we want to know what is **23% of 60**

The proportion would be **23/100 = x/60**

We will cross multiply 23(60) = 100 (x)

**1380 = 100x**

We will divide both sides by **100.**

1380/**100 = **100x**/100**

**13.8 = x (we will round to 14)**

Therefore if it take one person 6 hours to rake leaves and the other 7 hours to rake leaves.

It would take them **3 hours and 14 minutes** to rake the leaves together.

**The solution is 3 hours and 14 minutes.**

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