8.9: Trip Functions
Read the facts below and look at the table. Can you complete the table to show changes in Ms. Wilson's odometer? Can you write a rule that shows the relationship between the number of hours and the odometer reading? In this concept, we will learn to write rules for information given about trips.
Facts: Before the start of the crosscountry trip, the odometer in Mrs. Wilson’s car showed 4,100 miles. On the trip, she averaged 50 miles per hour.
Guidance
In order to make a table and write a rule for situations like the one above, we can use the problem solving steps to help.
 First, describe what you know. What did the odometer say at the beginning? How much is it changing each hour?
 Second, identify what your job is. In these problems, your job will be to make a table and write a rule.
 Third, make a plan. In these problems, your plan should be to use the facts to fill in the table. Then, look for a pattern to help you write the rule.
 Fourth, solve. Implement your plan.
 Fifth, check. Make sure your rule works with the facts.
Example A
Facts: Before he left on his trip, Mr. Patterson’s truck odometer showed 23,500 miles. He averaged 40 miles per hour on his drive from Sacramento to San Diego.

 First: Complete the table to show changes in Mr. Patterson’s truck odometer for the first 6 hours.

 Second: Write a rule that describes how the number of hours traveled is related to what the truck odometer shows.


 Rule: _______________________________________________________
Solution:
We can use problem solving steps and the facts above to solve this problem.
\begin{align*}& \mathbf{Describe:} && \text{Before the start of the trip, Mr. Patterson's truck odometer showed} \ 23,500\\ &&& \text{miles. On the trip, he drove an average of} \ 40 \ \text{miles each hour.}\\ \\ & \mathbf{My \ Job:} && \text{Use the facts to complete the table. Write a rule that shows how the}\\ &&& \text{number of miles on the odometer is related to the number of hours of}\\ &&& \text{travel on the trip.}\\ \\ & \mathbf{Plan:} && \text{Start with the table. Put 23,500 at 0 hours. Add} \ 40 \ \text{to} \ 23,500 \\ &&& \text{for each new hour. Then write the rule.} \end{align*}
\begin{align*}& \mathbf{Solve:} && \text{Rule: Number of miles is the sum of} \ 23,500 \ \text{and the product of number of}\\ &&& \text{hours and} \ 40 \ \text{mph.}\\ \\ & \mathbf{Check:} && \text{Use the rule and to verify the facts.}\\ &&& 23,500 + 1 \times 40=23,540\\ &&& 23,500 + 2 \times 40=23,580\\ &&& 23,500 + 3 \times 40=23,620\\ &&& 23,500 + 4 \times 40=23,660\\ &&& 23,500 + 5 \times 40=23,700\\ &&& 23,500 + 6 \times 40=23,740\end{align*}
Example B
Facts: The Karene City School Bus averaged 30 miles per hour on its trip to the state basketball competition. At the start of the trip, the bus’s odometer showed 72,160 miles.

 First: Complete the table to show changes in the bus’s odometer for the first 6 hours.

 Second: Write a rule that describes how the number of hours traveled is related to what the bus odometer shows.


 Rule: _______________________________________________________
Solution:
We can use problem solving steps and the facts above to solve this problem.
\begin{align*}& \mathbf{Describe:} && \text{Before the start of the trip, the Karene City School Bus odometer showed} \ 72,160\\ &&& \text{miles. On the trip, they drove an average of} \ 30 \ \text{miles each hour.}\\ \\ & \mathbf{My \ Job:} && \text{Use the facts to complete the table. Write a rule that shows how the}\\ &&& \text{number of miles on the odometer is related to the number of hours of}\\ &&& \text{travel on the trip.}\\ \\ & \mathbf{Plan:} && \text{Start with the table. Put 72,160 at 0 hours. Add} \ 30 \ \text{to} \ 72,160 \\ &&& \text{for each new hour. Then write the rule.} \end{align*}
\begin{align*}& \mathbf{Solve:} && \text{Rule: Number of miles is the sum of} \ 72,160 \ \text{and the product of number of}\\ &&& \text{hours and} \ 30 \ \text{mph.}\\ \\ & \mathbf{Check:} && \text{Use the rule and to verify the facts.}\\ &&& 72,160 + 1 \times 30=72,190\\ &&& 72,160 + 2 \times 30=72,220\\ &&& 72,160 + 3 \times 30=72,250\\ &&& 72,160 + 4 \times 30=72,280\\ &&& 72,160 + 5 \times 30=72,310\\ &&& 72,160 + 6 \times 30=72,340\end{align*}
Concept Problem Revisited
Facts: Before the start of the crosscountry trip, the odometer in Mrs. Wilson’s car showed 4,100 miles. On the trip, she averaged 50 miles per hour.
We can use problem solving steps and the facts above to solve this problem.
\begin{align*}& \mathbf{Describe:} && \text{Before the start of the trip, Ms. Wilson's car odameter showed} \ 4,100\\ &&& \text{miles. On the trip, she drove an average of} \ 50 \ \text{miles each hour. The table}\\ &&& \text{shows} \ 4,100 \ \text{miles at} \ 0 \ \text{hours.}\\ \\ & \mathbf{My \ Job:} && \text{Use the facts to complete the table. Write a rule that shows how the}\\ &&& \text{number of miles on the odometer is related to the number of hours of}\\ &&& \text{travel on the trip.}\\ \\ & \mathbf{Plan:} && \text{Start with the table. Add} \ 50 \ \text{to} \ 4,100 \ \text{for each new hour. Then write the}\\ &&& \text{rule.}\end{align*}
\begin{align*}& \mathbf{Solve:} && \text{Rule: Number of miles is the sum of} \ 4,100 \ \text{and the product of number of}\\ &&& \text{hours and} \ 50 \ \text{mph.}\\ \\ & \mathbf{Check:} && \text{Use the rule and to verify the facts.}\\ &&& 4,100 + 1 \times 50=4,150\\ &&& 4,100 + 2 \times 50=4,200\\ &&& 4,100 + 3 \times 50=4,250\\ &&& 4,100 + 4 \times 50=4,300\\ &&& 4,100 + 5 \times 50=4,350\\ &&& 4,100 + 6 \times 50=4,400\end{align*}
Vocabulary
One type of table shows a relationship between an input and an output. In this concept, the inputs of our tables were number of hours and the outputs of our tables were odometer: number of miles. A rule is an equation that can describe the relationship between the inputs and the outputs of a table. In this concept, we wrote rules that showed the relationship between the number of hours and the odometer or pedometer reading.
Guided Practice
1. Facts: Charlie’s pedometer is on his belt. It registers the number of miles walked. Before the hike, the pedometer showed 27 miles. Charlie hiked for several days and averaged 3 miles per hour.
 First: Complete the table to show changes in Charlie’s pedometer for the first 6 hours.
 Second: Write a rule that describes how the number of hours traveled is related to what the pedometer shows.
 Rule: _______________________________________________________
2. Facts: Before Brent left on his bike hike, his bike’s odometer showed 62 miles. Brent averaged 8 miles per hour.
 First: Complete the table to show changes in Brent’s bike odometer for the first 6 hours.
 Second: Write a rule that describes how the number of hours traveled is related to what the bike odometer shows.
 Rule: _______________________________________________________
Answers:
1. Rule: Number of miles is the sum of 27 and the product of number of hours and 3 mph.
2. Rule: Number of miles is the sum of 62 and the product of number of hours and 8 mph.
Practice
1. Facts: David’s pedometer is on his belt. It registers the number of miles walked. Before the hike, the pedometer showed 15 miles. David walked for several days and averaged 2 miles per hour.
 First: Complete the table to show changes in David’s pedometer for the first 6 hours.
 Second: Write a rule that describes how the number of hours traveled is related to what the pedometer shows.
 Rule: _______________________________________________________
2. Facts: Before Jason left on his bike, his bike’s odometer showed 27 miles. Jason averaged 10 miles per hour.
 First: Complete the table to show changes in Jason’s bike odometer for the first 6 hours.
 Second: Write a rule that describes how the number of hours traveled is related to what the bike odometer shows.
 Rule: _______________________________________________________
3. Facts: Anne got a new pedometer that tells her how many miles she has walked. One day the pedometer says 5 miles. Anne then does a long walkathon where she averages 3 miles per hour.
 First: Complete the table to show changes in Anne’s pedometer for the first 6 hours.
 Second: Write a rule that describes how the number of hours traveled is related to what the pedometer shows.
 Rule: _______________________________________________________
4. Facts: Katie's car odometer shows 31,570 before a long car trip. She then goes on a trip where she averages 55 miles per hour.
 First: Complete the table to show changes in Katie's car odometer for the first 6 hours.
 Second: Write a rule that describes how the number of hours traveled is related to what the bike odometer shows.
 Rule: _______________________________________________________
5. Facts: Bob is a bus driver for the city. The odometer on the bus shows 65,490 when he starts driving one day. He averages 15 miles per hour throughout the day.
 First: Complete the table to show changes in Bob's bus odometer for the first 6 hours.
 Second: Write a rule that describes how the number of hours traveled is related to what the bike odometer shows.
 Rule: _______________________________________________________
Image Attributions
Students use facts to complete tables and write rules that show the relationship between the input and the output of the tables. Students use problem solving steps to help.