Brian multiplied his average speed of 14.73 miles per hour by the amount of time he spent cross-country skiing. His product was 11.0475.
| Brian's Activity Time (hours) |
|---|---|
| Hiking | 3 |
| Mountain Biking | 1.45 |
| Horseback Riding | 1.2 |
| Cross-Country Sking | 0.75 |
Rounding to the nearest whole number, determine whether Brian's product is reasonable.
Round Brian's average speed to [$\square$].
Round the activity time to [$\square$].
Was Brian's product reasonable? [$\square$]
Answer (1)
Round Brian's average speed: 14.73 ≈ 15 .
Round the cross-country skiing time: 0.75 ≈ 1 .
Calculate the rounded product: $15
\times 1 = 15$.
Compare the rounded product (15) with the rounded original product (11): Brian's product is not reasonable. N o
Explanation
Problem Analysis Let's analyze the problem. Brian multiplied his average speed by the time he spent cross-country skiing, resulting in a product. We need to determine if this product is reasonable by rounding the average speed and time to the nearest whole number and comparing the rounded product to the original product (also rounded).
Rounding Average Speed First, we round Brian's average speed of 14.73 miles per hour to the nearest whole number. Since 0.73 is greater than 0.5, we round up to 15.
Rounding Activity Time Next, we round the cross-country skiing time of 0.75 hours to the nearest whole number. Since 0.75 is greater than 0.5, we round up to 1.
Calculating Rounded Product Now, we multiply the rounded average speed (15) by the rounded cross-country skiing time (1): 15 × 1 = 15
Rounding Original Product We are given that Brian's product was 11.0475. We round this to the nearest whole number. Since 0.0475 is less than 0.5, we round down to 11.
Reasonableness Check Finally, we compare the rounded product (15) with the rounded given product (11). Since 15 is not close to 11, Brian's product is not reasonable.
Final Answer Therefore:
Round Brian's average speed to 15.
Round the activity time to 1.
Was Brian's product reasonable? No.
Examples
Understanding reasonableness through estimation is useful in everyday life. For example, if you are buying multiple items at a store, you can quickly estimate the total cost by rounding each item's price to the nearest dollar and adding them up. This helps you ensure that the final bill is within a reasonable range and that there are no unexpected charges. Similarly, when calculating travel time, rounding the distance and speed can give you a quick estimate of how long the journey will take, helping you plan your day effectively.
