1
If a job can be done in t hours, then
Section 6.7: Using Rational
Equations
t
of
it can be done in 1 hour.
WORK PROBLEMS
1.
Ben can mow a lawn in 4 hours. Jerry can mow the same lawn in 5
hours. How long would it take them to mow the lawn together?
Let t represent the total number of hours it takes them together
Portion of lawn mowed
by Ben in 1 hour
2.
+
Portion of lawn mowed
Portion of lawn mowed
by Jerry in 1 hour
=
together in 1 hour
Stella can type one page in 10 minutes. Stanley can type one page in 15
minutes. How long will it take them, working together, to type 100
pages? Let t be the time, in minutes, that it takes them to finish 100
pages.
Stella’s rate
per minute
3.
+
Stanley’s rate
per minute
=
Rate together
per minute
Mr. Pardun’s swimming pool has 2 input pipes, A and B. Pipe A can fill
the pool three times as fast as Pipe B. Together both pipes can fill the
pool in 24 hours. Find the time it takes each pipe to fill the pool.
MOTION PROBLEMS
Remember: distance = rate * time (d = rt)
1. A car travels 55 mph and drives for 2 hours. How far did the car travel?
2. A rocket launches and travels 1500 miles in 2 hours. How fast was it
traveling?
3. One car travels 20 mph faster than another. While the faster car goes 240
miles, the slower car goes 180 miles. How fast is each car going?
d
r
t
slower car
faster car
4. A plane flies 2000 miles from Chicago to Los Angeles with a 50 mph tail wind
in 3 1/3 hours. Returning against the same wind, it takes 4 hours. What is
the speed of the plane if there is no wind?
d
With wind
Against wind
r
t
5. A boat travels 246 miles downstream in the same time it takes to travel 180
miles upstream. The speed of the current in the stream is 5.5 miles/hr. Find
the speed of the boat in still water.
d
r
t
Upstream
Downstream
6. Two canoeists paddle 10 km upstream in 5 hours. They make the return trip
in only 1 hour. Assuming that the canoeists paddle at a constant rate, what
is the speed of the current?
d
r
t
Upstream
Downstream
7. The sum of a number and 6 times its reciprocal is –5. Find the number.