Instructions
- Read the travel scenario and record all important information.
- Show your calculations, including units such as miles, hours, minutes, gallons, and dollars.
- Use these formulas when needed:
- Time = Distance ÷ Speed
- Fuel used = Distance ÷ Miles per gallon
- Fuel cost = Gallons used × Price per gallon
- 1 hour = 60 minutes
- 1 mile ≈ 1.6 kilometers
- Round money to the nearest cent and time to the nearest minute unless instructed otherwise.
- Complete the core questions first. Then try the optional challenge questions.
The Travel Mission
You are helping plan a 50-mile journey to a youth science festival. Your family is comparing two routes:
-
Route A: Scenic Route
- Speed: 40 miles per hour
- Car fuel efficiency: 25 miles per gallon
- Gas price: $3.60 per gallon
- Toll: $0
- Snack cost: $8.00
-
Route B: Express Route
- Speed: 60 miles per hour
- Car fuel efficiency: 30 miles per gallon
- Gas price: $3.60 per gallon
- Toll: $4.00
- Snack cost: $8.00
Assume the car travels at a steady speed and that the entire 50-mile journey is driven on each route.
Part 1: Speed and Distance Basics
-
What distance will the family travel on either route?
Answer: ____ miles
-
Which route has the greater speed? Circle one.
Route A Route B
-
How many more miles per hour is Route B than Route A?
Calculation: __
Answer: ____ miles per hour
-
Convert each speed to kilometers per hour. Use 1 mile ≈ 1.6 kilometers.
- Route A: 40 × 1.6 = ____ km/h
- Route B: 60 × 1.6 = ____ km/h
-
Match each measurement with the most appropriate unit. Write the letter on the line.
- _____ Distance traveled
- _____ Speed of the car
- _____ Amount of fuel used
- _____ Cost of the trip
A. gallons B. miles C. miles per hour D. dollars
Part 2: Calculate Travel Time
-
Use Time = Distance ÷ Speed to find the travel time for Route A.
Time = 50 ÷ 40 = ____ hours
-
Convert the decimal part of Route A's time into minutes.
Hint: 0.25 hour × 60 minutes = 15 minutes.
Route A travel time: ____ hours and ____ minutes
-
Find the travel time for Route B.
Time = 50 ÷ 60 = ____ hours
-
Convert Route B's travel time into minutes. Round to the nearest minute.
Calculation: __
Route B travel time: approximately ____ minutes
-
How much time is saved by choosing Route B instead of Route A?
Calculation: __
Time saved: ____ minutes
-
Explain in one or two sentences why the faster route does not take zero time, even though it saves time.
Part 3: Fuel and Travel Budget
-
Calculate the fuel used on Route A.
Fuel used = 50 ÷ 25 = ____ gallons
-
Calculate the fuel cost for Route A.
Fuel cost = ____ gallons × $3.60 = $____
-
Calculate the fuel used on Route B.
Fuel used = 50 ÷ 30 = ____ gallons
-
Calculate the fuel cost for Route B. Round to the nearest cent.
Fuel cost = ____ gallons × $3.60 = $____
-
Complete the travel budget organizer. The example row shows how to record one expense.
| Expense | Route A Cost | Route B Cost |
|---|---|---|
| Example: Snack | $8.00 | $8.00 |
| Fuel | ||
| Toll | ||
| Snack | ||
| Total trip cost | ||
| Difference in total cost |
-
Which route costs less overall? Circle one.
Route A Route B They cost the same
-
How much more or less does the faster route cost than the scenic route?
Answer: $____
-
Suppose the family has a travel budget of $20.00. Can the family afford either route? Explain using your totals.
Part 4: Make a Practical Decision
-
The family must arrive as quickly as possible, but they also want to spend as little as possible. Based on both time and cost, which route would you recommend?
Route I recommend: _____
Explain your decision using at least two facts from your calculations.
-
Imagine the family leaves at 9:20 a.m. What time will they arrive using Route A? Give your answer to the nearest minute.
Arrival time: ____
-
What time will they arrive using Route B? Give your answer to the nearest minute.
Arrival time: ____
-
The family has a festival workshop beginning at 10:30 a.m. Which route gives them more time to spare before the workshop?
Route: ____
Approximately how many minutes will they have to spare? ____ minutes
Optional Challenge
-
The family wants to save at least 20 minutes compared with Route A. What is the minimum average speed needed to complete the 50-mile journey in 55 minutes?
Hint: Convert 55 minutes to hours before dividing.
Calculation: __
Minimum speed: approximately ____ miles per hour
-
A third route travels at 50 miles per hour, uses 25 miles per gallon, has a $2.00 toll, and includes the same $8.00 snack. Calculate its travel time and total cost.
Travel time: ____
Total cost: $____
-
Create your own travel option. Choose a speed between 35 and 70 miles per hour and predict how long the 50-mile trip will take.
My speed: ____ miles per hour
My predicted time: ____
Show your calculation:
Reflection
-
Which calculation was most useful for making a travel decision: time, speed conversion, fuel cost, or total budget? Explain why.
Answer Key
-
50 miles
-
Route B
-
60 − 40 = 20 miles per hour
-
- Route A: 40 × 1.6 = 64 km/h
- Route B: 60 × 1.6 = 96 km/h
-
- Distance traveled: B
- Speed of the car: C
- Amount of fuel used: A
- Cost of the trip: D
-
50 ÷ 40 = 1.25 hours
-
0.25 × 60 = 15, so Route A takes 1 hour 15 minutes.
-
50 ÷ 60 = 0.8333 hour, or approximately 0.83 hour.
-
0.8333 × 60 = 50, so Route B takes approximately 50 minutes.
-
Route A takes 75 minutes and Route B takes 50 minutes. 75 − 50 = 25 minutes saved.
-
Sample answer: The car still has to travel the full 50 miles. A higher speed reduces the travel time, but it does not eliminate the distance.
-
50 ÷ 25 = 2 gallons
-
2 × $3.60 = $7.20
-
50 ÷ 30 = 1.6667 gallons, or approximately 1.67 gallons
-
1.6667 × $3.60 = $6.00, so the fuel cost is $6.00.
-
- Route A fuel: $7.20
- Route B fuel: $6.00
- Route A toll: $0.00
- Route B toll: $4.00
- Route A snack: $8.00
- Route B snack: $8.00
- Route A total: $7.20 + $0.00 + $8.00 = $15.20
- Route B total: $6.00 + $4.00 + $8.00 = $18.00
- Difference: $18.00 − $15.20 = $2.80
-
Route A
-
The faster route costs $2.80 more than the scenic route.
-
Yes, the family can afford either route. Route A costs $15.20 and Route B costs $18.00, both of which are less than $20.00.
-
Answers may vary. Sample answer: I recommend Route B if arriving quickly is most important because it saves 25 minutes. However, Route A is better for saving money because it costs $2.80 less.
-
Route A leaves at 9:20 a.m. and takes 1 hour 15 minutes, so the arrival time is 10:35 a.m.
-
Route B leaves at 9:20 a.m. and takes 50 minutes, so the arrival time is 10:10 a.m.
-
Route B gives more time to spare. From 10:10 a.m. to 10:30 a.m. is 20 minutes.
-
55 minutes = 55 ÷ 60 = 0.9167 hour. Speed = 50 ÷ 0.9167 = approximately 54.5 miles per hour.
-
Third route:
- Travel time: 50 ÷ 50 = 1 hour = 60 minutes
- Fuel used: 50 ÷ 25 = 2 gallons
- Fuel cost: 2 × $3.60 = $7.20
- Total cost: $7.20 + $2.00 + $8.00 = $17.20
-
Answers will vary. For example, at 50 miles per hour: 50 ÷ 50 = 1 hour.
-
Answers will vary. A strong answer explains how the selected calculation helped compare the routes in a realistic way.