Oven A takes five hours longer than oven B to bake y pizzas. If oven A

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

­Here are two additional ways to do this problem:

Method 1 (based on time):
A = x + 5 hrs for y pizzas
B = x for y pizzas

So for 3y/2 pizzas:
A = 3(x+5)/2
B = 3x/2

Total time then: 2/(3x+15) + 2/3x = 1/2 (Since 2 hours when they work together).

Solving for this gets the answer.

Method 2 (based on work):
A = x + 5 hrs for y pizzas
B = x for y pizzas

Time taken to work together: 2 hours
2/x + 2/(x+5) = 3/2

Solving for this gets the answer.

Time taken to bake y pizzas = 4.3 hrs > please explain this calculation and process in detail.

I'm assuming you meant to ask 4/3 hrs viz. time taken by A and B working together to bake y pizzas.

Since we are given that, oven A and B working together, time taken to bake \(\frac{3y}{2}\) pizzas is \(2\) hours, and we know that Rate * Time = Work

The Rate of A and B working together will be => Work / Time = \((3y/2)/2\) = \(\frac{3y}{4}\)

Now, time taken to bake y pizzas by oven A and B together will be => Work / Rate = \(\frac{y}{(3y/4)}\) = \(\frac{4}{3}\) hrs

Well, above calc. is not really required, if you approach it directly calculating (Rate of A + Rate of B) * Time taken working together = Work done working together

\((\frac{y}{t+5} + \frac{y}{t})*2 = \frac{3y}{2}\)

And get time taken by B for y pizzas, i.e. t = 5/3 hrs => 100 mins.

Hope it helps