blue dot printer can print one order of booklets in 4.5 hours red dot printer can do the same job in 5.5 hours how long will it take if both presses are used?
the first printer does 1 job in 4.5 hours, so its rate is $\displaystyle \frac {1 \text{ job}}{4.5 \text{ hours}} = \frac 29 \text{ job/hour}$
the second printer does 1 job in 5.5 hours, so its rate is $\displaystyle \frac {1 \text{ job}}{5.5 \text{ hours}} = \frac 2{11} \text{ job/hour}$
how long does it take them to complete 1 job together? well, they complete it at the sum of their rates. so we want $\displaystyle x$ such that:
$\displaystyle \frac 29 \text{ job/hour} + \frac 2{11} \text{ job/hour} = \frac {1 \text{ job}}{x \text{ hours}}$
thus we need to solve $\displaystyle \frac 29 + \frac 2{11} = \frac 1x$ for $\displaystyle x$. that will give us the number of hours
Lets set up the equation, we know that the Blue dot printer can complete one pamphlet per every 4.5 hours so it's rate is $\displaystyle \frac{1}{4.5}$
The red dot printer can complete 1 pamphlet in 5.5 hours so the red do printer rate is $\displaystyle \frac{1}{5.5}$
Setting up the equation we get
pamphlets made = rate of red dot * (time) + rate of blue dot * (time)
which is $\displaystyle 1=\frac{1}{4.5}t+\frac{1}{5.5}t$ and solving for our time t we get t=2.475 hours.
Hope that helps.
EASY!!
well, this is an inverse variation, the more the printers the less the work
so first add the reciprocal of the time then De-reciprocal the final answer
that is
1/4.5 + 1/5.5 = .....
multiply both fractions with 4.5 and 5.5 to get the same denominator
5.5+4.5/24.75
= 10/24.75
now reverse this answer
= 24.75/10
=2.475 hours
and tahts the final answer