Question

If a certain wheel turns at a constant rate of x revolutions per minute, how many revolutions will the wheel make in k seconds?

• A. 60kx
• B. kx
• C. x/k
• D. x/(60k)
• E. kx/60

Hint:

Always check for consistent units. When rate and time are given in different units (like minutes and seconds), convert one to match the other before you multiply.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This problem involves unit conversion. The rate is given in revolutions per minute, but the time is given in seconds. We must express both in compatible units before calculating the total revolutions.
Step 2: Key Formula or Approach:
Total Revolutions = Rate of Revolution \(\times\) Time
We need to convert the rate from revolutions per minute to revolutions per second.
Step 3: Detailed Explanation:
The given rate is \(x\) revolutions per minute.
Since there are 60 seconds in a minute, we can convert the rate to revolutions per second:
\[ \text{Rate} = \frac{x \text{ revolutions}}{1 \text{ minute}} = \frac{x \text{ revolutions}}{60 \text{ seconds}} \] The time given is \(k\) seconds.
Now we can calculate the total number of revolutions:
\[ \text{Total Revolutions} = \left( \frac{x}{60} \frac{\text{revolutions}}{\text{second}} \right) \times (k \text{ seconds}) \] \[ \text{Total Revolutions} = \frac{kx}{60} \] Step 4: Final Answer:
The wheel will make \(\frac{kx}{60}\) revolutions in \(k\) seconds. This corresponds to option (E).