Question

Working together, it takes two computers

20
minutes to send out a company's email. If it takes the slower computer
45
minutes to do the job on its own, how long will it take the faster computer to do the job on its own?

Answer 1

so hmmm if both computers can do the emailing in 20minutes, how much have they done in 1minute then?

well, it takes 20mins for the email to be sent by both computers, in 1minute then, they have done only 1/20th of the task

we know the rate of the slower computer, is 45mins, so in 1minute then, if it were to do it by itself, it'd had done 1/45th of the job

so, when they're both sending together, the slower one will still be doing 1/45th of the job within those 20mins, alongside the faster computer, whose rate we dunno.

so.. let's say the rate of the faster computer is 1/a, it has done 1/a'th of the task in 1minute

so... if we add both rates together, to see how much they have done in 1minute for 1/20th of the task, which took them 20mins to completion


`\bf \textit{rate of the slower computer}=\cfrac{1}{45} \\\\\\ \textit{rate of the faster computer}=\cfrac{1}{a} \\\\\\ \textit{in 1 minute they have done}=\cfrac{1}{20}\\\\ -----------------------------\\\\ \cfrac{1}{45}+\cfrac{1}{a}=\cfrac{1}{20}`

"a" is how much takes the faster computer to do it by itself, since in 1 minute it can do 1/a of the work

solve for "a"