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?

Question

Mathematics

Hammer

16 May, 20:10

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?

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Answers (1)

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Stephen Lucas · Answer 1

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!