Question

Toni makes apple pies for the local bakery. When Toni works with an assistant, she produces 60% more apple pies and works 20% fewer hours. Having an assistant increases Toni’s output of apple pies per hour by what percent?

Answer 1

Answer: η = 200 %

Explanation:

When Toni bakes alone, we have this: Toni bakes n apple pies in a time frame of t

This is mathematiclly expressed as:

output = produce/time

produce = n, time = t

output 1 = n/t     -------------------- Eqn 1  

When Toni bakes with an assistant, we have this: Toni bakes 60% more apple pies in a time frame shorter by 20%

This is mathematiclly expressed as:

produce = n + 0.6 n = 1.6 n, time = t - 0.2 t = 0.8 t

output 2 = 1.6 n/0.8 t     --------------- Eqn 2  

η = 100% x output 2/output 1

η = 100% x $\frac{1.6 n}{0.8 t}$/($\frac{n}{t}$)

η = 200 %

Answer 2

Answer:

200 % is the answer.

Explanation:

Toni makes x be apple pies .

and Jane works for y hours.

therefore, he makes x apple pies in y hours

which implies he makes $\frac{x}{y}$ apple pies per hour  

Now with help of an assistant:  

Toni  makes 60% more  apple pies  i.e. x + 0.6x = 1.6x  apple pies

works 20% less i.e. y - 0.2y = 0.8y hours

therefore, now together they make 1.6x/0.8y apple pies per hour $\frac{\frac{1.6x}{0.8y} }{\frac{x}{y} } X 100$

simplifying we get

200

Hence % increase in output PER HOUR is 200.