GmatKiss wrote:Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.
A. 20xz-y/(x+y)
B. y+z/(20xz)
C. 20x(y-z)/(x+y)
D. 20xy-z/(x+y)
E. y(20x-z)/(x+y)
Let one cake = 6 units.
Let x=3, implying that Pierre's rate = 6/3 = 2 units per hour.
Let y=2, implying that Franco's rate = 6/2 = 3 units per hour.
Since 1 cake = 6 units, 20 cakes = 120 units.
Let z=50 hours, implying that the number of units produced by Pierre alone = 2*50 = 100 units.
When elements work together, add their rates.
Thus, the time for Pierre and Franco together to produce the remaining 20 units = 20/(2+3) = 4 hours. This is our target.
Now we plug x=3, y=2 and z=50 into the answers to see which yields our target of 4.
Only answer choice
E works:
y(20x-z)/(x+y) = 2(20*3 - 50)/5 = 20/5 = 4.
The correct answer is
E.
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