if mary takes 3 hours to mow a lawn and sally takes 5 hours how long will it take them to mow it together
Mary's rate = lawn/3
Sally's rate = lawn/5
combined rate = lawn/3 + lawn/5
= 8lawn/15
time = lawn/(8lawn/15) = 15/8 or 1.875 hrs = 1 hour and about 53 minutes
To find out how long it will take Mary and Sally to mow the lawn together, you can use the concept of work rates.
Work rate is a measure of how fast a person can complete a task. The work rate is inversely proportional to the time taken to complete a task. In other words, the faster the work rate, the less time it takes to complete the task.
Let's calculate the work rates for Mary and Sally:
Mary's work rate = 1 lawn / 3 hours (she can mow 1 lawn in 3 hours)
Sally's work rate = 1 lawn / 5 hours (she can mow 1 lawn in 5 hours)
Now, to find their combined work rate, we add their individual work rates together:
Combined work rate = Mary's work rate + Sally's work rate
Combined work rate = 1/3 lawns per hour + 1/5 lawns per hour
To add these fractions, we need a common denominator:
Combined work rate = (5/15 + 3/15) lawns per hour
Combined work rate = 8/15 lawns per hour
Now that we have the combined work rate, we can calculate the time it takes for them to mow the lawn together:
Time = 1 lawn / Combined work rate
Time = 1 lawn / (8/15 lawns per hour)
Simplifying this equation:
Time = 1 lawn * (15/8) hours per lawn
Time = 15/8 hours
So, it would take them approximately 1 hour and 52.5 minutes (or 1.875 hours) to mow the lawn together.