Question 940919

if Kate could do {{{10}}} jobs in {{{20}}} minutes, then she could do at the rate  {{{ 10jobs/20min=(1/2)(job/min)}}}


and if Ethan could do {{{15}}} jobs in {{{35}}} minutes, he could do  at the rate {{{ 15jobs/35min=(3/7)(job/min)}}}

Let {{{t}}}=amount of time it takes them to do jobs working together.

Together, they could do jobs at the rate of {{{1/2+3/7=7/14+6/14=13/14}}}

So our equation to solve is:
{{{(13/14)t=30 }}}....... multiply each side by {{{14}}}

{{{14(13/14)t=30*14 }}}

{{{13t=420 }}}

{{{t=420/13 }}}

{{{t=32.31min }}}

{{{t=32min }}}and {{{18}}}seconds would take both Kate and Ethan to do {{{30}}} jobs