Question 198755
This is a problem of adding 2 rates to get a combined rate
In words,
Krystal's rate of working is (1 floor waxed)/(Krystal's time for 1 floor)
Perry's rate of working is (1 floor waxed)/(Perry's time for 1 floor)
and
If I add these rates to get a rate working together,
Krystal and Perry's rate of working is (1 floor waxed)/(K & P time for 1 floor)
and
The problem says that working together, (1 floor waxed)/(5.76 min)
Krystal's rate of working is (1 floor waxed)/ (16 min)
Let {{{t}}}= Perry's time to wax 1 floor working alone
{{{1/16 + 1/t = 1/5.76}}}
Multiply both sides by {{{1/100}}}
{{{1/1600 + 1/(100t) = 1/576}}}
Multiply both sides by {{{1600*576}}}
{{{576 + (16*576)/t = 1600}}}
Multiply both sides by {{{t}}}
{{{576t + 9216 = 1600t}}}
{{{1024t = 9216}}}
{{{t = 9}}}
Perry, working alone, can wax the floor in 9 minutes
check answer:
{{{1/16 + 1/t = 1/5.76}}}
{{{1/16 + 1/9 = 1/5.76}}}
{{{9/(16*9) + 16/(16*9) = 100/576}}}
{{{9/144 + 16/144 = 25/144}}}
{{{25/144 = 25/144}}}
OK