Question 387082
Think of these problems as adding their
rates of working separately
Let {{{R[1]}}} = Betsy's rate of working alone
Let {{{R[2]}}} = Mother's rate of working alone
Let {{{R[3]}}} = their rate of working together
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The rule is:
{{{R[1] + R[2] = R[3]}}}
given:
{{{R[1] = 1/4}}}
This means 1 room cleaned in 4 hours
{{{R[2] = 1/2}}}
This means 1 room cleaned in 2 hours
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So far I've got
{{{1/4 + 1/2 = R[3]}}}
I can express {{{R[3]}}} as {{{1/x}}}, or 1 room
cleaned in {{{x}}} hours
Now I have:
{{{1/4 + 1/2 = 1/x}}}
Multiply both sides by {{{4x}}}
{{{x + 2x = 4}}}
{{{3x = 4}}}
{{{x = 4/3}}} hours
This is the same as:
{{{(4/3)*60 = 80}}} min, or 1 hour and 20 minutes working together