Let the speed of Oscar be $v$ miles per hour (mph). Since Miguel can drive 6 times as fast, his speed is $6v$ mph.

The time it takes for Oscar to travel 54 miles is given by the formula:

$\text{Time for Oscar} = \frac{54}{v}$

Similarly, the time it takes for Miguel to travel 54 miles is:

$\text{Time for Miguel} = \frac{54}{6v}$

According to the problem, Oscar takes 3 hours longer than Miguel to travel the same distance, so:

$\frac{54}{v} = \frac{54}{6v} + 3$

Step 1: Solve the equation

First, subtract $\frac{54}{6v}$ from both sides:

$\frac{54}{v} - \frac{54}{6v} = 3$

Factor out $\frac{54}{v}$:

$\frac{54}{v} \left(1 - \frac{1}{6}\right) = 3$

Simplify the expression inside the parentheses:

$\frac{54}{v} \times \frac{5}{6} = 3$

Multiply both sides by $\frac{6}{5}$ to isolate $\frac{54}{v}$:

$\frac{54}{v} = \frac{18}{5}$

Now, solve for $v$ by multiplying both sides by $v$ and dividing by $\frac{18}{5}$:

$v = \frac{54 \times 5}{18}$

$v = 15 \, \text{mph}$

Thus, Oscar can ride his bicycle at 15 miles per hour.

Do you want further details or have any questions?

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5 Related Questions:

1. How would the result change if Oscar could ride 4 times slower than Miguel?
2. What if Oscar's speed was reduced by 10%? How would that affect the time difference?
3. How would you model this scenario if the distance was unknown but the time difference was still 3 hours?
4. If the distance were doubled, how would the speeds affect the travel times?
5. Can we determine the speeds if the time difference between Oscar and Miguel was given as a percentage?

Tip: Always remember to carefully define variables when working with rates and times to avoid confusion.