Amy can clean the house in 7 hours. When she works together with Tom, the job takes 5 hours. How long would it take Tom, working by himself, to clean the house?
Amy's rate = house/7
Tom's rate = house/x
combined rate = house/7 + house/x
= (xhouse + 7house)/(7x)
= house(x+7)/(7x)
then
house/[house(x+7)/(7x) = 5
1/[(x+7)/(7x)] = 5
7x/(x+7) = 5
7x = 5x+35
2x=35
x = 35/2 or 17.5 hours
check:
combined rate = 1/17.5 + 1/7 = 2/35 + 1/7 = 1/5
time = 1/(1/5) = 5
Can someone explain What percentage of the work did each person do?
Stop cheating on thinkwell !!
Well, if Amy can clean the house in 7 hours and when she works with Tom it takes them 5 hours, then I guess Tom is really good at avoiding housework! But let's get to the math. Let's assume that Tom takes x hours to clean the house by himself. So in 1 hour, Tom completes 1/x of the job, and Amy completes 1/7 of the job. When they work together, in 1 hour they complete 1/5 of the job. So we can set up the equation 1/x + 1/7 = 1/5. Now let's solve this equation and see how long it would take Tom to clean the house by himself. Trust me, Tom is not as slow as this equation!
To find out how long it would take Tom to clean the house by himself, we can use the concept of work rates.
Let's assign a work rate for Amy, which will be 1/7 of the job per hour since she can clean the house in 7 hours.
Now, since Amy and Tom are working together, their combined work rate is 1/5 of the job per hour because they can clean the house in 5 hours together.
Let's assign a work rate for Tom as x, which represents the fraction of the house he can clean in one hour.
So, Amy's work rate is 1/7 and Tom's work rate is x.
When they work together, their combined work rate is 1/5.
Using this information, we can create the following equation:
1/7 + x = 1/5
To solve for x, we need to isolate it on one side of the equation. We can do that by subtracting 1/7 from both sides:
x = 1/5 - 1/7
Finding a common denominator for the right-hand side gives:
x = 7/35 - 5/35
x = 2/35
So, Tom's work rate is 2/35 of the job per hour.
Now, to find out how long it would take Tom to clean the house by himself, we need to determine how many hours it would take him to complete the entire job, which is equivalent to his work rate being equal to 1.
So we can set up the equation:
2/35 = 1/x
To solve for x, we can observe that cross-multiplication can be used:
2x = 35
Finally, dividing both sides by 2 gives:
x = 35/2
Therefore, it would take Tom, working by himself, approximately 17.5 hours to clean the house.