Suppose that it takes Sally 3 hours to mow, and it takes Tom 4 hours to mow the same lawn; Tom's mower is less powerful than Sally's. Without using algebra determine how long it would take Sally and Tom to mow the lawn if they worked together using both lawn mowers. Comparing and scaling
hmmm. no algebra? How about
Sally can mow 4 lawns in 12 hours
Tom can mow 3 lawns in 12 hours
together they can mow 7 lawns in 12 hours.
So, that means 12/7 hours/lawn
To determine how long it would take Sally and Tom to mow the lawn together, we can use a concept called work rates.
First, let's consider Sally's work rate. Since it takes her 3 hours to mow the lawn alone, we can say that her work rate is 1/3 of the lawn per hour. This means that Sally can mow 1/3 of the lawn in one hour.
Similarly, Tom's work rate can be determined. As it takes him 4 hours to mow the same lawn, his work rate is 1/4 of the lawn per hour. This means that Tom can mow 1/4 of the lawn in one hour.
Now, to find their combined work rate when they work together, we can add their individual work rates. Sally's work rate is 1/3 of the lawn per hour, and Tom's work rate is 1/4 of the lawn per hour. Therefore, their combined work rate is 1/3 + 1/4 = 7/12 of the lawn per hour.
To determine the time it would take for Sally and Tom to mow the lawn together, we can take the reciprocal of their combined work rate. This means that it would take them 12/7 hours to mow the lawn together.
To simplify the answer, we can convert this into minutes. Since there are 60 minutes in an hour, multiplying 12/7 by 60 gives us approximately 102.86 minutes.
Therefore, if Sally and Tom work together using both lawn mowers, it would take them approximately 102.86 minutes to mow the lawn.