Rate Word Problems

Rate word problems involve understanding how different quantities relate to each other through rates, which can be speed, work, or other measurable factors. To solve these problems, we often use the formula:

ext{Rate} = rac{ ext{Distance}}{ ext{Time}}

Worked Example

Problem: A car travels 300 miles in 5 hours. What is the average speed of the car?

1. Identify the distance and time:

   • Distance = 300 miles
   • Time = 5 hours

2. Use the formula for rate:

   • Rate = Distance / Time

3. Substitute the values into the formula:

   • Rate = $\frac{300}{5}$

4. Perform the division:

   • Rate = 60 miles per hour

Conclusion: The average speed of the car is 60 miles per hour.

Key Questions

• If a cyclist covers 120 miles in 4 hours, what is their speed?
• A train travels at a speed of 80 miles per hour. How far will it travel in 3 hours?
• If a runner can complete a 5-mile race in 40 minutes, what is their average speed in miles per hour?
• A boat travels 150 miles upstream in 5 hours. What is its speed in still water if the current is 5 miles per hour?

Keywords

• Rate
• Speed
• Distance
• Time
• Average