Question

the sum of a number and its reciprocal is2 1/6 .find the number​

Answer 1

For the question on the mystery number, let x be the number.

 

x + 1/x = 13/6

 

6x2 - 13x + 6 = 0

 

(2x - 3)(3x - 2) = 0

 

x = 3/2 or 2/3

 

For the question with the secretary:

 

lcm(5,6) = 30

 

In 30 hours we have

 

Secretary 1: 600 envelopes

Secretary 2: 500 envelopes

Total: 1100 envelopes

 

So for 300 envelopes, the two secretaries working together need:

 

(300/1100)(30 hours) ≈ 8.18 hours