Modeling situations with rational functions

Question

STEVEN can rack the leaves from the backyard lawn five minutes faster then David. If they work together it takes them six minutes to rack the leaves from the lawn. Making their combined rate 1/6 lawn per minute. How long would it take david to rack the leaves from the backyard lawn, working alone?

Answer 1

Let David take x min

So steven will take (x-5) min

Rate of Davids work =1/x per min

Rate of steven work = 1/(x-5) per min

combined work

1/x +1/(x-5) = 1/6

6(2x-5) = x(x-5)

12x -30 = x² -5x

x² -17x +30 = 0

(x-15)(x-2) =0

x =15 or 2

David will take 15 min

x = 2 is not a valid value as Steven take 5 mins less time than Davis and 2-5 is negative.

x=15 or 2

Answer 2

David needs five minutes more than Steve

s represents the time Steve needs working alone

s + 5 represents the time David needs working alone

(6 / s) + (6 / [s + 5]) = 1

6(s + 5) + 6s = s(s + 5)

Can you solve for s and answer?