To solve this problem, we first need to determine the biker's speed and then use it to calculate how far they travel in 15 minutes.

Step 1: Find the Biker's Speed

The biker covers $\frac{3}{5}$ of a mile in $\frac{1}{3}$ of an hour.

To find the speed, we can use the formula for speed:

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

Substituting the given values:

$\text{Speed} = \frac{\frac{3}{5} \text{ miles}}{\frac{1}{3} \text{ hours}}$

To simplify this fraction, we multiply by the reciprocal of the denominator:

$\text{Speed} = \frac{3}{5} \times \frac{3}{1} = \frac{9}{5} \text{ miles per hour}$

Step 2: Convert 15 Minutes to Hours

15 minutes is equal to $\frac{15}{60}$ hours:

$\frac{15}{60} = \frac{1}{4} \text{ hours}$

Step 3: Calculate the Distance Traveled in 15 Minutes

Now we use the biker's speed to find out how far they travel in $\frac{1}{4}$ hour:

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

Substituting the values:

$\text{Distance} = \frac{9}{5} \text{ miles per hour} \times \frac{1}{4} \text{ hours}$

$\text{Distance} = \frac{9 \times 1}{5 \times 4} = \frac{9}{20} \text{ miles}$

Conclusion

The biker travels $\frac{9}{20}$ of a mile in 15 minutes.

Follow-up Questions:

1. How long will it take the biker to travel 2 miles at the same speed?
2. If the biker continues at the same speed, how far will they travel in 2 hours?
3. How long does it take the biker to cover 1 mile at the same speed?
4. What is the biker's speed in feet per second?
5. If the biker rests for 10 minutes after each 15-minute interval, how far will they travel in 1 hour?

Tip:

Always convert time units consistently when calculating speed and distance, especially when dealing with minutes and hours.