college algebra

Question

x/4 + x/6 = 1
Fraction of work done by Sue in x hours + Fraction of work done by Joe in x hours = 1 job completed

Answer 1

The unusual thing about “combination of work” problems is that we are given units such as “hours per job,” but must use “jobs per hour” to solve the problem.

For example, “If it takes Sue 4 hours to mow the lawn and it takes Joe 6 hours to mow the same lawn, how long will it take them when working together [each with a lawn mower]?”

Sue works at 4 hours per lawn, or (4 hrs)/(1 lawn). This is also ((1 lawn)/(4 hours)).

Now, if x is the time it takes the two of them working together, then Sue does:
                  (x hrs)*((1 lawn)/(4 hrs)) = (x/4) lawn
           Joe, working slower, does:

                  (x hrs)(*(1 lawn)/(6 hrs)) = (x/6) lawn

When they are combined [again, PLZ notice the very important units]:
        Sue’s portion       +         Joe’s portion    =     1 lawn
          (x/4) lawn         +           (x/6) lawn     =     1 lawn


          x/4     +     x/6    =    1                 [lawn cancels]
           3x     +      2x    =   12                [multiply by LCM of 12]

                   5x            =    12
                   x    =     12/5

                   x    = 2 2/5

They work together for 2 2/5 hours [that is, 2.4 hours, or 2 hours 24 minutes].

Answer 2

Plugging in random numbers gives you 2.4 / 4 + 2.4 / 6 = 1, or 0.6+0.4 = 1 (2.4 / 4 = 0.6; 2.4 / 6 = 0.4)

Now, to get to the answer properly, put the fractions in a common denominator. 6 x 4 = 24, so (something / 24) + (something / 24) = 1.

In this case, X will be multiplied by the denominator of the term with which it's reconciling, so we get:

(6x / 24) + (4x / 24) = 1.

Add the two terms;

10x / 24 = 1.

Multiply both sides by the new denominator to eliminate the fraction;

(10x / 24) x 24 = 10x, 1 x 24 = 24

10x = 24

Divide both sides by 10,

X = 2.4

Answer 3

Would you like to solve for x?  MULTIPLY ALL TERMS BY 12 (the LCD) and this will become easy:

3x + 2x = 12.