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.