Exercises with Solutions

Chapter 7
Rational Functions
27. Let t represent the unknown time, r represent Amelie’s rate (reports/hour), and
s represent Jean’s rate. Using the relationship
this leads to the following three equations:
work = rate · time,
Amelie: 1 = r(t + 18)
Jean: 1 = st
together: 1 = (r + s) 12
Solve for r and s in the first two equations, and then plug those values into the third
equation to obtain
( 1
1 =
t + 18 + 1 )
12
t
Now solve this rational equation for t:
( 1
1 =
t + 18 + 1 )
12 =⇒ t(t + 18) = 12t + 12(t + 18)
t
=⇒ t 2 + 18t = 24t + 216
=⇒ t 2 − 6t − 216 = 0
=⇒ (t − 18)(t + 12) = 0
=⇒ t = 18 hours
29. Let t represent the unknown time, r represent Ricardo’s rate (reports/hour), and
s represent Sanjay’s rate. Using the relationship
this leads to the following three equations:
work = rate · time,
Ricardo: 1 = r(t + 12)
Sanjay: 1 = st
together: 1 = (r + s) 8
Solve for r and s in the first two equations, and then plug those values into the third
equation to obtain
( 1
1 =
t + 12 + 1 )
8
t
Version: Fall 2007