```Question 313379
Linda drove to her boyfriend's house and found him waxing his car. This job usually takes him 3 hours. She wanted her boyfriend to take her to the show which was starting in 2 hours. She offered to help him, but she knew she would need 4 hours to wax the car by herself. She wondered how long both of them would need to wax the car. Calculate the number of hours it will take. (Round your answer to the nearest tenth.)
<pre><font size = 4 color = "indigo"><b>
Make this chart
Number of      Time      Rate in
Cars waxed   Required    cars/hr.
Linda alone         |             |          |
---------------------------------------------------------
bf alone            |             |          |
----------------------------------------------------------
Linda & bf together |             |          |

We want to to know the time for both Linda and her bf working
together to wax the car.   So we let x represent this time
and put x for the time required for them working together to
wax 1 car.  So fill in x for their time working together and
1 for the number of cars they can wax in x hours working
together.

Number of      Time      Rate in
Cars waxed   Required    cars/hr.
Linda alone         |             |          |
--------------------|-------------|----------|-----------
bf alone            |             |          |
--------------------|-------------|----------|------------
Linda & bf together |      1      |     x    |

Linda's bf can wax 1 car in 3 hours, so we place 1 for the
number of cars and 3 for his number of hours:

Number of      Time      Rate in
Cars waxed   Required    cars/hr.
Linda alone         |             |          |
--------------------|-------------|----------|-----------
bf alone            |      1      |     3    |
--------------------|-------------|----------|------------
Linda & bf together |      1      |     x    |

Linda can wax 1 car in 4 hours, so we place 1 for the
number of cars and 4 for her number of hours:

Number of      Time      Rate in
Cars waxed   Required    cars/hr.
Linda alone         |      1      |     4    |
--------------------|-------------|----------|-----------
bf alone            |      1      |     3    |
--------------------|-------------|----------|------------
Linda & bf together |      1      |     x    |

Now we fill in the rates in cars/hr. by dividing the number of
cars by the number of hours.

Number of      Time      Rate in
Cars waxed   Required    cars/hr.
Linda alone         |      1      |     4    |    1/4
--------------------|-------------|----------|-----------
bf alone            |      1      |     3    |    1/3
--------------------|-------------|----------|------------
Linda & bf together |      1      |     x    |    1/x

We for the equation from this:

Linda's rate + bf's rate = their rate together:

1/4    +    1/3    =     1/x

{{{1/4+1/3=1/x}}}

Can you solve that? If not post again asking how.

You get {{{12/7}}}hrs or {{{1&5/7}}}hrs, about 1 hour and 43 minutes.
So it it doesn't take more than 17 minutes to drive and get seated at
the show, they can still make it.  But of course they could just go in
her car and finish waxing his car after the show. :-)

Edwin</pre>  ```