Bill can mow his mother's lawn in 45 minutes. His brother Jim can mow it in 75 minutes. How long will it take them to do it together?
Can someone help with with the work? But also an explanation of how it works? I want to understand this so I don't miss it on the test.
Bill's rate = 1lawn/45
Jim's rate = 1lawn/75
combined rate = 1lawn/45 + 1lawn/75
= 8lawn/228
time at combined rate = 1lawn/(8lawn/225)
= 1lawn (225/8lawn)
= 225/8
= 28.125 minutes
notice the "lawn" divided out, so we could really have used anything at all.
Some students simply use 1 as the unit of whatever the task is.
so combined rate = 1/45 + 1/75 = 8/225
time at combined rate = 1/(8/225)
= 225/8 = 28.125
if you had 3 rates involved, you would get a combined rate by simply adding up the 3 rates, etc
To find out how long it will take Bill and Jim to mow the lawn together, we can use the concept of rates.
First, we need to determine the rates at which Bill and Jim mow the lawn individually. Bill takes 45 minutes to mow the lawn, so his rate is 1 lawn per 45 minutes, which can be written as:
Bill's rate = 1/45 lawns per minute.
Similarly, Jim takes 75 minutes to mow the lawn, so his rate is 1 lawn per 75 minutes, which can be written as:
Jim's rate = 1/75 lawns per minute.
To find the combined rate when they work together, we need to add their rates:
Combined rate = Bill's rate + Jim's rate.
Now, we can calculate the combined rate:
Combined rate = 1/45 + 1/75.
To add these fractions, we need to find a common denominator, which is the least common multiple (LCM) of 45 and 75. The LCM of 45 and 75 is 225.
So, let's rewrite the fractions with the common denominator of 225:
Combined rate = (5/225) + (3/225).
Now, we can add the fractions:
Combined rate = 8/225.
The combined rate of Bill and Jim working together is 8/225 lawns per minute.
To find out how long it will take them to mow the lawn together, we can rewrite the rate as a time per lawn:
Time = 1/combined rate.
Substituting the value of the combined rate:
Time = 1 / (8/225).
Dividing 1 by 8/225:
Time = 225/8.
Simplifying the fraction:
Time = 28.125 minutes.
Therefore, it will take Bill and Jim approximately 28.125 minutes to mow the lawn together.