Speed Route Quest Answer Key

This worksheet gives students practice using constant rates of speed to find missing distances or travel times. The problems include buses, cyclists, trains, boats, delivery vans, and hikers. In each situation, the speed stays constant, so students use the relationship between distance and time to solve for the unknown amount. Some problems ask how far something travels in a new amount of time, while others ask how long it will take to travel a new distance.

For a parent, the key idea is that the rate stays the same. If a bus travels 90 miles in 2 hours, then it travels 45 miles in 1 hour. Once the child knows that unit rate, finding the distance for 5 hours becomes much easier. Other problems may be solved just as easily with a proportion.

Learning Goals

• Find Constant Rates: Students determine the distance traveled per unit of time.
• Solve for Distance: Learners use the rate to find how far an object travels.
• Solve for Time: Students work backward to determine how long a trip takes.
• Use Unit Rates or Proportions: Learners choose a proportional method that works.
• Apply Ratios to Travel: Students connect proportional reasoning to speed situations.

Parent-Friendly Teaching Tips

One simple method is to find the distance for 1 hour first.

For example:

90 miles in 2 hours

90 ÷ 2 = 45 miles per hour

For 5 hours:

45 × 5 = 225 miles

So the bus travels 225 miles.

For a time question:

75 miles in 3 hours

75 ÷ 3 = 25 miles per hour

To travel 125 miles:

125 ÷ 25 = 5 hours

Why This Worksheet Helps

• Builds Rate Understanding: Students see speed as a relationship between distance and time.
• Strengthens Unit-Rate Skills: Finding the “per hour” value often makes the problem simpler.
• Connects Math to Travel: The situations are easy to visualize.
• Practices Working Forward and Backward: Students solve for either distance or time.
• Prepares for More Advanced Rate Problems: Constant-speed reasoning appears frequently in algebra and science.

The main value of this worksheet is that it teaches students to recognize that when speed stays constant, distance and time change proportionally. Rates, division, multiplication, time, and distance all work together. For parents, the best question is: “How much happens in one hour, and how can we use that to answer the new question?”