Zeno takes 20 min longer to decorate a dozen cupcakes than it takes Lia. When th

Question

Zeno takes 20 min longer to decorate a dozen cupcakes than it takes Lia. When they work together, it takes them 49.5 min. How long would each take to do the job alone? Zeno takes 20 min longer to decorate a dozen cupcakes than it takes Lia. When they work together, it takes them 49.5 min. How long would each take to do the job alone? Zeno takes 20 min longer to decorate a dozen cupcakes than it takes Lia. When they work together, it takes them 49.5 min. How long would each take to do the job alone?

Explanation / Answer

Time taken by Lia t1 = X

Time taken by Zeno t2 = X + 20

When they work together total time will be calculated by.

t1*t2/(t1 + t2) = t

X*(X + 20)/(X + X + 20) = 49.5

X^2 + 20X = 99X + 990

X^2 - 79X - 990 = 0

Solving this equation gives,

X = 90 min

t1 = 90 min

t2 = 90 + 20 = 110 min

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