Question 650191
Let x=amount of time it takes Ev to do the dishes
Then Ev works at the rate of 1/x of the dishes per minute
It takes John x+5 minutes to do the dishes
Then John works at the rate of 1/(x+5) of the dishes per minute
Together they work at the rate of 1/x +1/(x+5) of the dishes per minute but we know that together they work at the rate of 1/20 of the dishes per minute
So our equation to solve is:
1/x +1/(x+5)=1/20  multiply each term by 20x(x+5)
20(x+5)+20x=x(x+5)  simplify
20x+100+20x-x^2+5x and this gives us
x^2-35x-100=0  quadratic in standard form --solve using quadratic formula
 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
 {{{x = (35 +- sqrt( (-35)^2-4*(-100)))/(2) }}}
{{{x = (35 +- sqrt( 1225+400))/(2) }}}
{{{x = (35 +- sqrt( 1625))/(2) }}}
{{{x = (35 +- 40.3)/(2) }}}
{{{x = (35 +40.3)/(2) }}} and
{{{x = (35-40.3)/(2) }}}-----disregard--- this is a negative number
so we have:
x=37.65 min---amount of time it takes Ev to wash the dishes working alone
x+5=37.65+5=42.65 min --time it takes John working alone
CK
1/(37.65) + 1/(42.65)=1/20  I hope it does
Another way to check this problem:
20/(37.65) + 20/(42.65) should equal 1 (one set of dishes, that is)

Hope this helps--ptaylor