To solve this problem, we can use the formula for distance:

$\text{Distance} = \text{Speed} \times \text{Time}$

Given:

• Speed = 12 miles per hour (mi/h)
• Time = $1 \frac{1}{4}$ hours = $1 + \frac{1}{4} = 1.25$ hours

Now, multiplying the speed by the time:

$\text{Distance} = 12 \times 1.25 = 15 \, \text{miles}$

Final Answer:

The cyclist traveled 15 miles.

Would you like further explanation, or have any additional questions?

Here are five related questions:

1. How would the distance change if the speed was doubled but the time remained the same?
2. What would the cyclist's speed need to be to cover 20 miles in the same time?
3. How long would it take the cyclist to travel 30 miles at the same speed?
4. What is the cyclist’s average speed if they traveled 15 miles in 2 hours?
5. How many miles would the cyclist travel in 3 hours at a speed of 12 mi/h?

Tip: When dealing with fractions in word problems, it's often easier to convert them to decimals before multiplying!