# Math Help - Another problem I posted, but not getting it.

1. ## Another problem I posted, but not getting it.

Bill can do a jobin 3.8 j, and john can do the same job in 5.4h. How will it take them to do the job together? ROUND your answer to the nearest quarter of an hour??
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.
Joanne

Bill can do a jobin 3.8 j, and john can do the same job in 5.4h. How will it take them to do the job together? ROUND your answer to the nearest quarter of an hour??
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.
Joanne
Multiply by $\frac{10}{10}$ to clear the decimal

$\frac{10}{38} + \frac{10}{54}$

Spoiler:
The LCD of 38 and 54 is 1026

Bill can do a jobin 3.8 j, and john can do the same job in 5.4h. How will it take them to do the job together? ROUND your answer to the nearest quarter of an hour??
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.
Joanne
The rate at which they work together is the sum of those rates.
How you handle "fractions with decimals" depends upon whether you want to do them as fractions or as decimals!

To add 1/3.8+ 1/5.4 as fractions, multiply both numerator and denominator by 10: 10/38+ 10/54, simplify, 5/19+ 5/27, get common denominators and add: (5)(27)/(19)(27)+ 5(19)/(19)(27)= 135/513+ 95/513= 230/513.

To add 1/3.8+ 1/5.4 as decimals, convert to decimals: 1 divided by 3.8 is 0.26316 to five decimal places, and 1 divided by 5.4 is 0.18518, again to five decimal places. Their sum is 0.44834.

In any case, after you have the rate at which they work to gether on a given job, that is "jobs per hour", you get the time it takes to do the job together by inverting- "230/513 jobs per hour" gives "513/230 hours per job".
Likewise "0.44834 jobs per hour" gives "1/0.44834 hours per job". Both give, to five decimal places, 2.23043 hours.