# Algebra

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1) Mio can build a large shed in 15 days less than Yuuko can. If they build it together, it would take them 18 days. How long would it take each of them working alone?

M: Y:

2) A sink can be filled by a pipe in 6 minutes but it takes 12 minutes to drain a full sink. If both the pipe and the drain are open, how long will it take to fill the sink?

• Algebra -

a)

ratecombined=rateM+rateY
shed/18 = shed/(timeY-15) + shed/timeY

Y* (Y-15)=18( Y + (y-15))
y^2-15Y=36Y-270
y^2-51Y+270=0
(y-45)(Y-6)=0

y=45, M=30

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