Bob mosw his lawn in 3 hours, Jane can mow the same lawn in 5 hours. How much time would it take for them to mow the lawn together?
This is a problem in which you need to convert the work rate into something addable.
If Bob does his lawn in 3 hours, he does 1/3 in one hour. Similarly Jane can mow 1/5 of the lawn in one hour.
So in one hour, both working together will mow (1/3)+(1/5)=8/15 of the lawn.
The time it takes to mow the complete lawn is therefore 1/(8/15)=15/8=1 7/8 hours.
Thank you so much!
You're welcome!
To find out how much time it would take for Bob and Jane to mow the lawn together, we can use the concept of work.
Let's calculate the work rate of Bob and Jane individually. The work rate is equal to the amount of work done in a unit of time. In this case, the work rate is expressed in terms of lawns mowed per hour.
Bob mows the lawn in 3 hours, so his work rate is 1 lawn / 3 hours = 1/3 lawns per hour.
Jane mows the lawn in 5 hours, so her work rate is 1 lawn / 5 hours = 1/5 lawns per hour.
Now, to find the combined work rate of Bob and Jane, we can add their individual work rates:
Combined work rate = Bob's work rate + Jane's work rate
= 1/3 lawns per hour + 1/5 lawns per hour
To add the fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15.
Combined work rate = (5/15) lawns per hour + (3/15) lawns per hour
= 8/15 lawns per hour
So, Bob and Jane can mow the lawn together at a combined work rate of 8/15 lawns per hour.
To find the time it would take for them to mow the lawn together, we can use the formula:
Time = 1 / Combined work rate
Time = 1 / (8/15) lawns per hour
= 15/8 hours
Therefore, it would take Bob and Jane approximately 1 hour and 52.5 minutes to mow the lawn together.