SOLUTION: Together, Diane and Craig can mow their lawN in 1 hour and 10 minutes. Working alone, Diane can mow the lawn in 2 hours. How long will it take Craig to mow the lawn when working al

Question 980634: Together, Diane and Craig can mow their lawN in 1 hour and 10 minutes. Working alone, Diane can mow the lawn in 2 hours. How long will it take Craig to mow the lawn when working alone?
Found 2 solutions by josgarithmetic, josh_jordan:
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
Mow rate in unit of LAWN per HOUR.

The combined rate of Diane and Craig together is the sum of their individual rates. Craig's rate is unknown.

Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
We know that when they work together, they can complete the lawn job in 1 hour and 10 min, which is the same as 7/6 of an hour (1 hour and 10 min = 70 minutes. 70 minutes/60 minutes = 7/6). We normally are asked to find out how long it would take 2 people to do 1 job if each works at a certain rate. For instance, if our question said, "It takes John 3 hours to mow the lawn and it takes Suzy 4 hours to mow the lawn, how long would it take them to work together?" We would set the equation up as follows:

In our case, we already know how long it takes them to work together (7/6 hours), but we don't know how long it takes Craig to mow the lawn working alone. So, where the x's are in our normal equation, we would put 7/6 in it's place. In the denominator of the fraction representing Craig, we would list an x, so the equation would look like the following:

Now we would solve for x.

First, we can multiply our equation by the LCD of our fractions, which is 2x. Multiplying our entire equation by 2x would give us:

Next, multiply our equation by 6 to get rid of all of our fractions. This will give us:

Subtract 7x from both sides, which will give us:

----->

Divide both sides of the equation by 5, which will give us:

----->

It will take Craig 2.8 hours to mow the lawn when working alone. To convert 2.8 hours to hours and minutes, just multiply 60 by .8:

So, it will take Craig 2 hours and 48 minutes to mow the lawn when working alone.

ANSWER: 2 hrs 48 min
RELATED QUESTIONS
Craig and Pam, working together, can mow the lawn in 9 hours. Working alone, Pam takes... (answered by stanbon,lwsshak3)
Cara and Craig, working together, can mow the lawn in 8 hours. Working alone, Craig takes (answered by ikleyn)
pam and craig, working together, can mow the lawn in 8 hours. working alone craig takes... (answered by josgarithmetic)
Fred can mow the lawn in 1 hour. John can mow the lawn in 2 hours. How long will it take... (answered by stanbon)
twin brothers, andy and brian, can mow their grandparents lawn together in 30 minutes.... (answered by josgarithmetic)
Steve Dalton can mow his lawn in 4 hours. His sister Diane can now the same lawn in 3... (answered by JulietG,richwmiller)
Stephen and Kyle are brothers. Stephen can mow the lawn in 1 hour. Kyle takes 2 hours to... (answered by richwmiller)
Pam and John, working together, can mow the lawn in 2 hours. Working alone, John takes... (answered by josmiceli)
Working together, Dan and Leah an mow a lawn in one hour and twelve minutes. Working... (answered by josmiceli)