Bill can mow his mothers lawn in 6 minutes. His brother Jim can mow it in 9 minutes. How long will it take them to do it together, if each has his own lawnmower? (record answer in minutes rounded to one decimal place. For example 14.2835 minutes, record 14.3).
Bill's rate = lawn/6
Jim's reate = lawn/9
combined rate = lawn/6 + lawn/9
=5lawn/18
Time for combined effort = lawn/[5lawn/18]
= 18/5 minutes
= 3.6 minutes
Notice that "lawn" canceled, so we could have used any constant for "lawn"
in general for individual times of a,b,c,.. units of time
the time for a combined effort would be
1/[1/a + 1/b + 1/c + ...] units of time
To solve this problem, we can calculate the "work rate" of Bill and Jim and then use it to find the time it takes for them to mow the lawn together.
First, we need to determine the work rate of each individual. The work rate is the amount of work (in this case, mowing the entire lawn) done by a person in a given amount of time.
For Bill, we are told that he can mow his mother's lawn in 6 minutes. Therefore, his work rate is 1 lawn / 6 minutes, or 1/6 lawns per minute.
For Jim, we are told that he can mow the same lawn in 9 minutes. So, his work rate is 1 lawn / 9 minutes, or 1/9 lawns per minute.
Now, to find the combined work rate of Bill and Jim, we add their individual work rates together:
Combined work rate = Bill's work rate + Jim's work rate
Combined work rate = 1/6 lawns per minute + 1/9 lawns per minute
To simplify this, we need to find a common denominator for 6 and 9, which is 18. So, we can rewrite the combined work rate as:
Combined work rate = (3/18) lawns per minute + (2/18) lawns per minute
Combined work rate = 5/18 lawns per minute
Next, we can invert the combined work rate to find the time it takes for them to mow the lawn together:
Time = 1 / Combined work rate
Plugging in the combined work rate, we get:
Time = 1 / (5/18) lawns per minute
Time = (18/5) minutes
Therefore, it will take them approximately 3.6 minutes (rounded to one decimal place) to mow the lawn together.