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Oven A takes five hours longer than oven B to bake y pizzas. If oven A
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13 Feb 2023, 14:25
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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
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Joined: 22 Dec 2016
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Re: Oven A takes five hours longer than oven B to bake y pizzas. If oven A
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13 Feb 2023, 22:22
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Laila12618 wrote:
Oven A takes 5 hrs longer than oven B to bake y pizzas. If oven A + oven B can bake 3y/2 pizzas together in 2 hrs, approximately how long (in minutes) does it take to 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
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
Re: Oven A takes five hours longer than oven B to bake y pizzas. If oven A
[#permalink]
14 Feb 2023, 12:13
gmatophobia wrote:
Laila12618 wrote:
Oven A takes 5 hrs longer than oven B to bake y pizzas. If oven A + oven B can bake 3y/2 pizzas together in 2 hrs, approximately how long (in minutes) does it take to 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
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
I would like to understand better where this \(\frac{t(t+5)}{t + t + 5}\) comes from.
I understand t and t+5, but I don't understand how and why the fraction is built.
Could you please clarify?