ElementaryAlgebra2e-WEB_3zxfu3Z-76

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Truck going West
Truck going East
Table 3.16
Step 7. Answer the question with a complete sentence. It will take the trucks 2.5 hours to be 325 miles apart.
Table 3.17
TRY IT 3.99 Pierre and Monique leave their home in Portland at the same time. Pierre drives north on the
turnpike at a speed of 75 miles per hour while Monique drives south at a speed of 68 miles per
hour. How long will it take them to be 429 miles apart?
TRY IT 3.100 Thanh and Nhat leave their office in Sacramento at the same time. Thanh drives north on I-5 at
a speed of 72 miles per hour. Nhat drives south on I-5 at a speed of 76 miles per hour. How
long will it take them to be 330 miles apart?
Matching Units in Problems
It is important to make sure the units match when we use the distance rate and time formula. For instance, if the rate
is in miles per hour, then the time must be in hours.
EXAMPLE 3.51
When Katie Mae walks to school, it takes her 30 minutes. If she rides her bike, it takes her 15 minutes. Her speed is three
miles per hour faster when she rides her bike than when she walks. What are her walking speed and her speed riding
her bike?
Solution
First, we draw a diagram that represents the situation to help us see what is happening.
We are asked to find her speed walking and riding her bike. Let’s call her walking speed r. Since her biking speed is three
miles per hour faster, we will call that speed We write the speeds in the chart.
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The speed is in miles per hour, so we need to express the times in hours, too, in order for the units to be the same.
Remember, one hour is 60 minutes. So:
Next, we multiply rate times time to fill in the distance column.
The equation will come from the fact that the distance from Katie Mae’s home to her school is the same whether she is
walking or riding her bike.
So we say:
Translate into an equation.
Solve this equation.
Clear the fractions by multiplying by the LCD of all the fractions in
the equation.
Simplify.
6 mph
(Katie Mae's biking speed)
Let's check if this works.
Walk 3 mph (0.5 hour) = 1.5 miles
Bike 6 mph (0.25 hour) = 1.5 miles
Yes, either way Katie Mae travels 1.5 miles to school. Katie Mae’s walking speed is 3 mph.
Her speed riding her bike is 6 mph.
TRY IT 3.101 Suzy takes 50 minutes to hike uphill from the parking lot to the lookout tower. It takes her 30
minutes to hike back down to the parking lot. Her speed going downhill is 1.2 miles per hour
faster than her speed going uphill. Find Suzy’s uphill and downhill speeds.
TRY IT 3.102 Llewyn takes 45 minutes to drive his boat upstream from the dock to his favorite fishing spot. It
takes him 30 minutes to drive the boat back downstream to the dock. The boat’s speed going
3.5 • Solve Uniform Motion Applications 367
downstream is four miles per hour faster than its speed going upstream. Find the boat’s
upstream and downstream speeds.
In the distance, rate, and time formula, time represents the actual amount of elapsed time (in hours, minutes, etc.). If a
problem gives us starting and ending times as clock times, we must find the elapsed time in order to use the formula.
EXAMPLE 3.52
Hamilton loves to travel to Las Vegas, 255 miles from his home in Orange County. On his last trip, he left his house at
2:00 pm. The first part of his trip was on congested city freeways. At 4:00 pm, the traffic cleared and he was able to drive
through the desert at a speed 1.75 times as fast as when he drove in the congested area. He arrived in Las Vegas at 6:30
pm. How fast was he driving during each part of his trip?
Solution
A diagram will help us model this trip.
Next, we create a table to organize the information.
We know the total distance is 255 miles. We are looking for the rate of speed for each part of the trip. The rate in the
desert is 1.75 times the rate in the city. If we let the rate in the city, then the rate in the desert is
The times here are given as clock times. Hamilton started from home at 2:00 pm and entered the desert at 4:30 pm. So
he spent two hours driving the congested freeways in the city. Then he drove faster from 4:00 pm until 6:30 pm in the
desert. So he drove 2.5 hours in the desert.
Now, we multiply the rates by the times.
By looking at the diagram below, we can see that the sum of the distance driven in the city and the distance driven in the
desert is 255 miles.
Translate into an equation.
Solve this equation.
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Check.
Hamilton drove 40 mph in the city and 70 mph in the desert.
TRY IT 3.103 Cruz is training to compete in a triathlon. He left his house at 6:00 and ran until 7:30. Then he
rode his bike until 9:45. He covered a total distance of 51 miles. His speed when biking was 1.6
times his speed when running. Find Cruz’s biking and running speeds.
TRY IT 3.104 Phuong left home on his bicycle at 10:00. He rode on the flat street until 11:15, then rode uphill
until 11:45. He rode a total of 31 miles. His speed riding uphill was 0.6 times his speed on the
flat street. Find his speed biking uphill and on the flat street.
SECTION 3.5 EXERCISES
Practice Makes Perfect
Solve Uniform Motion Applications
In the following exercises, solve.
283. Lilah is moving from
Portland to Seattle. It
takes her three hours to
go by train. Mason leaves
the train station in
Portland and drives to the
train station in Seattle
with all Lilah’s boxes in his
car. It takes him 2.4 hours
to get to Seattle, driving
at 15 miles per hour
faster than the speed of
the train. Find Mason’s
speed and the speed of
the train.
284. Kathy and Cheryl are
walking in a fundraiser.
Kathy completes the
course in 4.8 hours and
Cheryl completes the
course in 8 hours. Kathy
walks two miles per hour
faster than Cheryl. Find
Kathy’s speed and
Cheryl’s speed.
285. Two busses go from
Sacramento for San
Diego. The express bus
makes the trip in 6.8
hours and the local bus
takes 10.2 hours for the
trip. The speed of the
express bus is 25 mph
faster than the speed of
the local bus. Find the
speed of both busses.
3.5 • Solve Uniform Motion Applications 369
286. A commercial jet and a
private airplane fly from
Denver to Phoenix. It
takes the commercial jet
1.1 hours for the flight,
and it takes the private
airplane 1.8 hours. The
speed of the commercial
jet is 210 miles per hour
faster than the speed of
the private airplane. Find
the speed of both
airplanes.
287. Saul drove his truck 3
hours from Dallas
towards Kansas City and
stopped at a truck stop to
get dinner. At the truck
stop he met Erwin, who
had driven 4 hours from
Kansas City towards
Dallas. The distance
between Dallas and
Kansas City is 542 miles,
and Erwin’s speed was
eight miles per hour
slower than Saul’s speed.
Find the speed of the two
truckers.
288. Charlie and Violet met for
lunch at a restaurant
between Memphis and
New Orleans. Charlie had
left Memphis and drove
4.8 hours towards New
Orleans. Violet had left
New Orleans and drove 2
hours towards Memphis,
at a speed 10 miles per
hour faster than Charlie’s
speed. The distance
between Memphis and
New Orleans is 394 miles.
Find the speed of the two
drivers.
289. Sisters Helen and Anne
live 332 miles apart. For
Thanksgiving, they met at
their other sister’s house
partway between their
homes. Helen drove 3.2
hours and Anne drove 2.8
hours. Helen’s average
speed was four miles per
hour faster than Anne’s.
Find Helen’s average
speed and Anne’s average
speed.
290. Ethan and Leo start riding
their bikes at the opposite
ends of a 65-mile bike
path. After Ethan has
ridden 1.5 hours and Leo
has ridden 2 hours, they
meet on the path. Ethan’s
speed is six miles per
hour faster than Leo’s
speed. Find the speed of
the two bikers.
291. Elvira and Aletheia live 3.1
miles apart on the same
street. They are in a study
group that meets at a
coffee shop between their
houses. It took Elvira half
an hour and Aletheia two-
thirds of an hour to walk
to the coffee shop.
Aletheia’s speed is 0.6
miles per hour slowerthan Elvira’s speed. Find
both women’s walking
speeds.
292. DaMarcus and Fabian live
23 miles apart and play
soccer at a park between
their homes. DaMarcus
rode his bike for three-
quarters of an hour and
Fabian rode his bike for
half an hour to get to the
park. Fabian’s speed was
six miles per hour faster
than DaMarcus’ speed.
Find the speed of both
soccer players.
293. Cindy and Richard leave
their dorm in Charleston
at the same time. Cindy
rides her bicycle north at
a speed of 18 miles per
hour. Richard rides his
bicycle south at a speed
of 14 miles per hour. How
long will it take them to
be 96 miles apart?
294. Matt and Chris leave their
uncle’s house in Phoenix
at the same time. Matt
drives west on I-60 at a
speed of 76 miles per
hour. Chris drives east on
I-60 at a speed of 82 miles
per hour. How many
hours will it take them to
be 632 miles apart?
295. Two busses leave Billings
at the same time. The
Seattle bus heads west on
I-90 at a speed of 73 miles
per hour while the
Chicago bus heads east at
a speed of 79 miles an
hour. How many hours
will it take them to be 532
miles apart?
296. Two boats leave the same
dock in Cairo at the same
time. One heads north on
the Mississippi River while
the other heads south.
The northbound boat
travels four miles per
hour. The southbound
boat goes eight miles per
hour. How long will it take
them to be 54 miles
apart?
297. Lorena walks the path
around the park in 30
minutes. If she jogs, it
takes her 20 minutes. Her
jogging speed is 1.5 miles
per hour faster than her
walking speed. Find
Lorena’s walking speed
and jogging speed.
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