Chapter 7 - Section 7.6 - Proportions and Problem Solving with Rational Equations - Exercise Set - Page 540: 52

6 2/3 hours

1st person: finishes job in 4 hours (does 1/4 of job in an hour) 2nd person: finishes job in x hours (does 1/x of job in an hour) combined job takes 2.5 hours (4/10 of job is done in an hour) $1/4 + 1/x = 4/10$ $40(1/4 + 1/x = 4/10)$ $10 + 40/x = 160/10$ $10 + 40/x = 16$ $40/x = 6$ $40=6x$ $40/6 =6x/6$ $40/6 = x$ $1/4 + 1/x = 4/10$ $1/4 + 1/(20/3) = 4/10$ $1/4 + 3/20 = 4/10$ $20(1/4 + 3/20 = 4/10)$ $5 + 3 = 80/10$ $5+3=8$