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13 Feb 2023, 14:25
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
62% (03:14) correct
38%
(03:13)
wrong
based on 419
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Oven A takes five hours longer than oven B to bake y pizzas. If oven A and oven B, working together at their respective constant rates, can bake 3y/2 pizzas in two hours, approximately how long (in minutes) does it take oven B to bake y pizzas?
(A) 80
(B) 90
(C) 100
(D) 110
(E) cannot be determined
Posted from my mobile device
(A) 80
(B) 90
(C) 100
(D) 110
(E) cannot be determined
Posted from my mobile device
14 Feb 2023, 12:48
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joaomesq1
Oven B takes t hours to bake y pizzas; therefore, in one hour the over bakes \(\frac{y}{t}\) pizzas
Oven A takes (t+5) hours to bake y pizzas; therefore, in one hour the over bakes \(\frac{y}{(t+5)}\) pizzas
Therefore Both ovens together will bake \(\frac{y}{t }+ \frac{y}{t+5}\) pizzas
Let's take t * (t+5) as the LCM of the two fractions, hence the fraction \(\frac{y}{t }+ \frac{y}{t+5}\) can now be represented as
\(\frac{y(t) + y(t + 5)}{t(t+5)}\)
\(\frac{y(t + t + 5)}{t(t+5)}\)
Thus, both ovens together will bake \(\frac{y(2t + 5)}{t(t+5)}\) pizzas one hour
Working together, both the ovens can bake one pizza in = \(\frac{t(t+5)}{y(2t + 5)}\) hours
Time taken to bake y pizzas = y * Time taken to bake 1 pizza
= \(\frac{t(t+5)}{y(2t + 5)} * y\) hours
Cancel y from numerator and denominator to get
= \(\frac{t(t+5)}{(2t + 5)}\) hours
General Discussion
13 Feb 2023, 22:22
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Laila12618
Given
Oven A + Oven B together can bake 3y/2 pizzas in 2 hours
Time taken to bake y pizzas = \(\frac{2 * 2 }{ 3}\) hours = \(\frac{4}{3}\) hours
Assume :
Time Oven B takes to bake y pizzas = t hours
Time Oven A takes to bake y pizzas = t+5 hours
Time taken when both Oven A and Oven B works together to bake y pizzas = \(\frac{t(t+5)}{t + t + 5}\)
\(\frac{t(t+5)}{2t + 5} = \frac{4}{3}\)
\(3t^2 + 7t -20 = 0\)
\(3t^2 + 12t - 5t - 20 = 0\)
(t+4)(3t-5) = 0
t = \(\frac{5}{3}\) hours
Time in minutes = \(\frac{5}{3} * 60 = 100\) mins
Option C
