Question

it takes birth three times as long as phone to set up a new alarm system together they can set up in 90 minutes how long would it take following to set up the new alarm system by himself make answer very clear

Answer 1

Well, first off, I don't ever recall anyone named "birth" or "phone", so let's just call them B and P.

so B is slower than P, say P can do the whole job in "p" minutes, and since B is three times as slow, then B can do it in "3*p" or "3p" minutes.

we know that they together can do it in 90 minutes, so in 1 minute alone, both of their rates added up, have only done 1/90 of the job, whilst P has done 1/p of the work and B has done 1/3p of the work.

$\bf \stackrel{B's~rate}{\cfrac{1}{3p}}+\stackrel{P's~rate}{\cfrac{1}{p}}~~=~~\cfrac{1}{90}\impliedby \begin{array}{llll} \textit{let's multiply both sides by }\stackrel{LCD}{90p}\\ \textit{to do away with the denominators} \end{array} \\\\\\ 90p\left( \cfrac{1}{3p}+\cfrac{1}{p} \right)~~=~~90p\left( \cfrac{1}{90} \right)\implies 30+90=p\implies 120=p$

 so it takes 120 minutes or 2 hours for P to do it alone, and 3p to B to do it alone.