A biker covers ⅗ of a mile in ⅓ hour. How far does the biker go in 15 minutes

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.

Learn how to calculate the distance a biker travels in 15 minutes with a detailed solution. This problem involves calculating speed, converting time units, and applying the distance formula. Suitable for high school students learning about speed and distance calculations.

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