Solving Rational Equations – Applications
Current problems ( water or wind):
distance = rate X time
(or) time = distance
rate
(or) rate = distance
time
Example 1: A jet travels 3950 mi from Chicago to London and 3950 mi on the return trip.
The total flying time is 16.5 h. The return trip takes longer due to winds that generally
blow from west to east. If the jet’s average speed with no wind is 485 mi/h, what is the
average speed of the wind during the round-trip flight? Round to the nearest mile per
hour?
D
R
T
Trip there
Return trip
Example 2: A motorboat can travel 20 mi/h in still water. If the boat can travel
3 mi downstream on a river in the same time it takes to travel 2 mi upstream, what is
the rate of the river’s current?
D
downstream
upstream
R
T
Work problems: If 2 entities are working on the same job, and the 1st would take ‘a’ hours to complete the job alone and the 2 nd ‘b’ hours
to complete the job alone, then use this equation to find ‘t’ the time it will take to complete the job:
1 + 1 = 1
a
b
t
Example 3: Layne can finish a 500-piece puzzle in about 8 hours. When Layne and
Kaylee work together, they can finish a 500-piece puzzle in about 4.5 hours. About
how long will it take Kaylee to finish a 500-piece puzzle if she works by herself?
Example 4: Marquez can mulch a garden in 20 minutes. Together Marquez and
Thekiso can mulch the same garden in 11 minutes. How long will it take Thekiso to
mulch the garden when working alone?
1. A restaurant has two pastry ovens. When both ovens are used, it takes about 3 hours to bake the bread needed for one day. When only
the large oven is used, it takes about 4 hours to bake the bread for one day. Approximately how long would it take to bake the bread for
one day if only the small oven were used?
2. A river barge travels at an average of 8 mi/h in still water. The barge travels 60 mi up the Mississippi River and 60 mi down the river in a
total of 16.5 h. What is the average speed of the current in this section of the Mississippi river? Round to the nearest tenth.
3. A small jet has an airspeed (the rate in still air) of 300 mi/h. During one day’s flights, the pilot notes that the plane could fly 85 mi with a
tailwind in the same time it took to fly 65 mi against that same wind. What was the rate of the wind?
4. Each month Kristen must make copies of a budget report. When she uses both the large and the small copier, the job takes 30 min. If
the small copier is broken, the job takes her 50 min. How long will the job take if the large copier is broken?
5. Marissa and Drayton took a canoeing trip, traveling 6 mi upsteam along a river, against a 2 mi/h current. They then returned
downsteam to the starting point of their trip. If their entire trip took 4 h, what was their rate in still water?
Work and Motion Problems Quiz
name _____________________________________period_____
MAKE A TABLE FOR EACH. SHOW YOUR ALGEBRA STEPS.
1. A glassblower can produce a set of simple glasses in about 2 h. When the glassblower works with an apprentice, the job takes about 1.5
h. How long would it take the apprentice to make a set of glasses when working alone? Whole number.
2 and 3. Sarah can bicycle 75 mi in the same time it takes her to drive 165 mi. If her driving rate is 30 mi/h faster than her rate on the
bicycle, find each rate. For number 2 Enter her DRIVE rate and for number 3 enter her BIKE rate. Both to the whole number.
4. Phoenix, an electrician, can wire a house in 20 h. If he works with Isa, the same job can be completed in 12 h. How long would it take
Isa, working alone, to wire the house? Whole number
5. Sadie and Kimberly are catering food for a wedding. Sadie can prepare the food in 5 hours and Kimberly takes 4.5 hours to do the same
job. How long it would take them to prepare the food together? Enter to the TENTH!!
6. On a river, a kayaker travels 2 mi upstream and 2 mi downstream in a total of 5 h. In still water, the kayaker can travel at an average
speed of 2 mi/h. Based on this information, what is the average speed of the current of this river? Round to the nearest tenth.