Accelerated Algebra II
Section 5.9 day 2
Goal: To solve word problems containing fractional equations.
Solve.
1. The sum of a number and its reciprocal is
26
. Find the number.
5
2. Find two positive numbers that differ by 8 and whose reciprocals differ by
1
.
6
1
3. The reciprocal of one third of a number decreased by one third of the reciprocal of the number is 3 .
Find the number.
4. Brett usually takes 50 minutes to groom the horses. After working 10 minutes, he was joined by
Angela and they finished the grooming in 15 minutes. How long would it have taken Angela working
alone?
5. Our pump can empty the swimming pool in 7 h less time than a smaller second pump can. Together
they can empty the pool in 12 h. How much time would it take the larger pump alone to empty it?
6. Because of strong headwinds, an airplane’s ground speed for the first half of a 2000 km trip averaged
only 600 km/h. What must its ground speed be for the rest of the trip if it is to average 720 km/h for the
entire trip? (hint: we do not know the time for either part of the trip so use time = distance/rate
Homework:
1. The sum of a number and its reciprocal is
25
. Find the number.
12
2. Find two numbers who sum is 25 and the sum of whose reciprocals is
1
.
6
3. The reciprocal of half a number increased by half the reciprocal of the number is ½. Find the number.
4. Stan can load his truck is 24 minutes. If his brother helps him, it takes them 15 minutes to load the
truck. How long does it take Stan’s brother alone?
5. One printing machine works twice as fast as another. When both machines are used, they can print a
magazine in 3 hours. How many hours would each machine require to do the job alone?
6. During 60 mi of city driving, Jenna average 15 mi/gal. She then drove 140 mi on an expressway and
averaged 25 mi/gal for the entire 200 miles. Find the average fuel consumption on the expressway.
(hint use time= distance/rate)
Answers:
4 3
1) or
3 4
2) 4 and 12
3) 5
4) 40 minutes
5) 4.5 h; 9 h
6) 35 mi/gal