Question

A certain number of special spells must be cast to protect the secret hiding place of the Order of the Phoenix. Each member of the Order is capable of casting the same number of these spells per hour. If two wizards were to join the Order, casting the protection spells can be completed in three hours instead of four hours. How many wizards are in the Order?

Answer 1

Answer: There are 6 wizards in the order.

Explanation:

Let's suppose that:

Let's define S as the rate at which each wizard casts the spells.

Let's suppose also that there are N wizards in the order.

We know that the N wizards can complete the task in 4 hours, then:

(N*S)*4h = 1

(the 1 represents the completed task)

And we know that if 2 more wizards joined, the total task would be completed in 3 hours, then we have the equation:

(N+2)*S*3h = 1

Then we have the system of equations:

(N*S)*4h = 1

(N+2)*S*3h = 1

And we want to find the value of N.

To start, we need to isolate S in one of the equations, i will isolate S in the first equation:

S = (1/N*4h)

Now we can replace this in the second equation, to get:

(N+2)*(1/N*4h)*3h = 1

(N + 2)*3/(4*N) = 1

Now we can solve this for N.

(3/4) + 6/(4N) = 1

Now we can multiply by N in both sides to get:

(3/4)*N + 6/4 = N

6/4 = N - (3/4)*N = (1/4)*N

(6/4)*4 = N

6 = N

There are 6 wizards in the order.