To solve this problem, we will first calculate the estimated time using the rounded values, and then we'll find the exact time.

Step 1: Estimated Answer

1. Speed of the object:
   The speed is given as $10$ and $1/10$ miles per hour, which is approximately $10.1$ mi/h.

2. Distance to be traveled:
   The distance is given as $4$ and $9/10$ miles, which is approximately $4.9$ miles.

3. Estimated time to travel:
   Using the formula $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$, we get: $\text{Time}_{\text{est}} = \frac{4.9 \, \text{mi}}{10.1 \, \text{mi/h}} \approx 0.485 \, \text{hours}.$

   Rounding to the nearest integer: $\text{Estimated time} \approx 0 \, \text{hours}.$

Step 2: Exact Answer

Now, we calculate the exact time using the provided values without rounding.

1. Exact speed:
   The speed is $10 \frac{1}{10} = 10.1 \, \text{mi/h}$.

2. Exact distance:
   The distance is $4 \frac{9}{10} = 4.9 \, \text{mi}$.

3. Exact time:
   Using the same formula $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$: $\text{Time}_{\text{exact}} = \frac{4.9 \, \text{mi}}{10.1 \, \text{mi/h}} = 0.4851 \, \text{hours}.$

Thus, the exact time is approximately $0.4851$ hours or about $29.1$ minutes.

Summary:

• Estimated time: 0 hours (after rounding).
• Exact time: $0.4851$ hours or $29.1$ minutes.

Would you like more details on any part of the solution?

Here are 5 related questions:

1. How can I convert time in hours to minutes?
2. What is the difference between estimated and exact values in real-world problems?
3. How do you round numbers to the nearest integer?
4. What other units can be used for speed and distance in such calculations?
5. How does changing speed affect the time to travel a fixed distance?

Tip: When rounding numbers, always check if the digit following the place you're rounding to is 5 or higher, as this will increase the rounded value.