Need help with word rational equation problem.

[bradycat]

Hi there,
I have 2 questions.

Bill can do a job in 3.8 h, and john can do the same job in 5.4 h. How will it take them to do the job together? ROUND your answer to the nearest quarter of an hour??
Answer in time?
I know you add 1/3.8+1/5.4 = time on how long it will take to do together.

I have looked online to show how to add fractions with decimals, when you have to find the LCD to cancel them out.
That is what I don't know how to do.
Please explain fully on how it is done please and thanks.
Joanne

 

[soroban]

Hello, bradycat!

Bill can do a job in 3.8 hours, and John can do the same job in 5.4 hours.
How will it take them to do the job together?
(Round your answer to the nearest quarter of an hour}

\(\displaystyle \text{Bill does the job in: }\,3.8 \:=\:\frac{38}{10} \:=\:\frac{19}{5}\text{ hours.}\)
\(\displaystyle \text{In one hour, he can do: }\:\frac{1}{\frac{19}{5}} \:=\:\frac{5}{19}\text{ of the job.}\)
\(\displaystyle \text{In }x\text{ hours, he can do }\:\frac{5x}{19}\text{ of the job.}\)

\(\displaystyle \text{John does the job in: }\,5.4 \:=\:\frac{54}{10} \:=\:\frac{27}{5}\text{ hours.}\)
\(\displaystyle \text{In one hour, he can do: }\:\frac{1}{\frac{27}{5}} \:=\:\frac{5}{27}\text{ of the job.}\)
\(\displaystyle \text{In }x\text{ hours, he can do: }\:\frac{5x}{27}\text{ of the job.}\)

\(\displaystyle \text{Together, in }x\text{ hours, they can do: }\:\frac{5x}{19} + \frac{5x}{27}\text{ of the job.}\)

\(\displaystyle \text{But in }x\text{ hours, they will have completed the job (1 job).}\)

\(\displaystyle \text{There is our equation }\;\hdots\quad \frac{5x}{19} + \frac{5x}{27} \:=\:1\)

 

[chrisr]

Here's another way

Bill can do 10 of that job in 38 hours (probably not without breaks which we won't count).
John does 10 in 54 hours.
Working together, Bill does 10 in the first 38 hours and 16(10)/38 in the remaining 16 hours,
while John does 10 jobs in 54 hours.
Together, that's 920/38 jobs in 54 hours,
corresponding to 1 job in 54(38)/920 hours = 2.23 hours approximately.

As 0.25 is a quarter, then rounded it's 2 and a quarter hours.