Question

John can mow the golf course in 7-hours.Larry can mow it in 5 hours. Form a rational equation that can be used to determine how long it would take to mow the golf course if they worked together?

Answer 1

There are a couple of ways of doing this one way is to say john does 1/7 per hour and Larry does 1/5 per hour so together (1/7+1/5)x=1 where x is the number of hours

Answer 2

can you help me on one more it's kind of similar?

Answer 3

The equation would be set up like this:
\[\frac{ 1 }{ 7 }+\frac{ 1 }{ 5 }=\frac{ 1 }{ t }\]

Answer 4

Solve for t, how long it takes them to complete the job together.

Answer 5

It would take them just a hair under 3 hours to get the job done together.

Answer 6

1 over 12

Answer 7

No. The common denominator is 35.

Answer 8

so 5 over 35 plus 7 over 35

Answer 9

\[\frac{ 5 }{ 35 }+\frac{ 7 }{ 35 }=\frac{ 1 }{ t }\]

Answer 10

\[\frac{ 12 }{ 35 }=\frac{ 1 }{ t }\]

Answer 11

Cross multiply to get 12t = 35, and t = 2.91666667

Answer 12

can you help me on one more it is almost the same thing. I can do it I think but I may need your help

Answer 13

Absolutely!

Answer 14

should I make a new post or same one?

Answer 15

This is fine!

Answer 16

Janice can clean the yard 1 hour faster than Pete can. If they work together the yard can be cleaned in 4 hours. Form a rational equation that can be used to determine how long it would take pete to clean the yard himself. What is the common denominator of your equation?

Answer 17

Ok, after much checking and double-checking, I got it. I would hate to ever do anything incorrectly and then have there be a gross misunderstanding!! Here's what I did:
We don't know how long it takes Pete to do the job, so, in accordance with a "work" problem, we will note his work being done as 1/t, t being the time it takes him to do the job (unknown). We also know that Janice can do the job in one less hour than it takes Pete. So her rate of work, based on Pete's, is 1/t - 1. This means she works one hour less than Pete. With me so far?

Answer 18

\[Pete=\frac{ 1 }{ t }\]
\[Janice=\frac{ 1 }{ t }-1\]

Answer 19

"t" is what we are looking for...the time it takes Pete to do the job on his own, right?

Answer 20

yes I got you

Answer 21

So with that information, we know that when they work together, ie adding their equations together, we get 4 hours. So...
\[\frac{ 1 }{ t }+(\frac{ 1 }{ t }-1)=4\]

Answer 22

Now we have a basic math problem to solve here:
\[\frac{ 1 }{ t }+\frac{ 1 }{ t }-1=4\]
and
\[\frac{ 2 }{ t }=5\]
and\[\frac{ 2 }{ t }=\frac{ 5 }{ 1 }\]

Answer 23

Now cross multiply. What do you get t to be equal to?

Answer 24

2 over 5t

Answer 25

This is beautiful the way it works out so perfectly, it really is.

Answer 26

Ok, here's the part where I might lose you so pay attention!

Answer 27

The ultimate goal is to figure out Pete's rate of work, right? His equation is
\[\frac{ 1 }{ t }\] but t = 2/5, so the equation you need to solve is
\[\frac{ 1 }{ t}=\frac{ 1 }{ \frac{ 2 }{ 5 } }\]

Answer 28

That is the same as rewriting it
\[\frac{ 1 }{ 1 }\times \frac{ 5 }{ 2 }=\frac{ 5 }{ 2 }=2.5\]

Answer 29

That is some basic math skill stuff that you need to know before you get to this point in Algebra. Do you get that part?

Answer 30

yeah I know that. I have to go somewhere right now when I come back can I message you and I finish the problem?

Answer 31

This tells us that Pete does the job himself in 2 1/2 hours, and Janice does it in one hour less which is 1 1/2 hours, and 2.5 + 1.5 = 4, which is how long it takes them to do the job together, according to the problem.

Answer 32

The denominator, obviously, is t.