A regular postal clerk sorts 100 letters in c seconds while a part time worker recquires p seconds to sort 100 letters. How many seconds will they recquire to sort 100 letters working together? Options: (A)p+c/2 (B)p+c/2 (C)pc/p+c (D)100(p+c)/pc (E) 100pc/p+c?

C

Step-by-step explanation:

100/c + 100/p

The formula is

r₁*t + r₂*t = total

r₁*t + r₂*t = 100 letters

So let's plug in everything. We're solving for the t.

100/c * t + 100/p * t = 100

t (100/c + 100/p) = 100

t = 100/ (100/c + 100/p)

t = 100 / 100(1/c + 1/p)

t = 1 / (1/c + 1/p)

Rationalize the denominator by multiplying 1/c * p/p and 1/p * c/c.

t = 1 / (p/pc + c/pc)

t = 1 / (p + c /pc)

Now we can flip it over.

t = pc / p+c

The answer is C!