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

Algebra ->  Rate-of-work-word-problems -> 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      Log On


   

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) About Me  (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.

1%2F2%2B1%2Fx=1%2F1%261%2F6

Answer by josh_jordan(263) About Me  (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:

%28x%2F3%29%2B%28x%2F4%29=1

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:

%28%287%2F6%29%2F2%29%2B%28%287%2F6%29%2Fx%29=1

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:

%28%287x%29%2F6%29%2B%2814%2F6%29=2x

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

7x%2B14=12x

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

14+=+12x+-7x -----> 14=5x

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

14%2F5=x ----->2.8=x

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:

60%2A.8=48

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

ANSWER: 2 hrs 48 min