Bill can mow the lawn in 2 hours, and his younger brother Tom can mow it in 3 hours. If both brothers mow the lawn together, how many hours will it take them?
i got that i would take one hour and 12 minutes
1/x = 1/2 + 1/3
solving for 'x' we have x=1.2
2* 60 = 12
it would take them 1 hour and 12 minutes to mow the lawn togethr
it would be x=8-T783
Well, let me pull out my clown calculator and do some math for you. If Bill can mow the lawn in 2 hours and Tom can mow it in 3 hours, we can calculate their combined mowing speed.
Bill's mowing speed is 1/2 lawns per hour (since he can mow the entire lawn in 2 hours), while Tom's mowing speed is 1/3 lawns per hour. So, when they mow together, they will be able to mow at a combined speed of 1/2 + 1/3 = 5/6 lawns per hour.
To figure out how long it will take them to mow the lawn together, we can take the reciprocal of their combined mowing speed, which is 6/5 hours. In minutes, that would be 6/5 * 60 = 72 minutes. So you're right, it would take them 1 hour and 12 minutes to mow the lawn together.
Good job on the math! Keep up the clown-tastic work!
To solve this problem, we need to find the rate at which each brother mows the lawn. We can use the formula:
Rate = Work / Time
Let's denote Bill's rate as "Rb" and Tom's rate as "Rt".
Bill can mow the lawn in 2 hours, so his rate is:
Rb = 1 lawn / 2 hours
Tom can mow the lawn in 3 hours, so his rate is:
Rt = 1 lawn / 3 hours
Now, let's find the combined rate when both brothers mow the lawn together. We can add their rates:
Combined Rate (Rc) = Rb + Rt
Rc = 1/2 + 1/3
To add these fractions, we need a common denominator. The common denominator of 2 and 3 is 6.
Rc = 3/6 + 2/6
Rc = 5/6
Now, we know that the combined rate (Rc) is 5/6 lawns per hour.
We can use the formula:
Time = Work / Rate
To find how long it will take both brothers to mow the lawn together, we set the work to 1 lawn (since they have to mow the entire lawn):
Time = 1 lawn / (5/6 lawns per hour)
To divide by a fraction, we multiply by its reciprocal:
Time = 1 lawn * (6/5 lawns per hour)
Simplifying, we get:
Time = 6/5 hours
Converting this to hours and minutes, we have:
Time = 6/5 * 60 minutes/hour
Time = 72 minutes
Therefore, if both brothers mow the lawn together, it will take them 1 hour and 12 minutes.