A straight road slopes steadily upwards. If the road rises 8m (to the nearest metre) over a horizontal distance of 120m (to the nearest 10m), what is the maximum possible gradient of the road? What is the minimum possible gradient? Give your answers to 3 significant figures.

The gradient of a road is calculated as the vertical rise over the horizontal distance. Mathematically, it is expressed as:

\[
\text{Gradient} = \frac{\text{Vertical Rise}}{\text{Horizontal Distance}}
\]

In this case, the vertical rise is given as 8 meters, and the horizontal distance is 120 meters, both rounded to the nearest values. To find the **maximum** and **minimum** gradients, we need to consider the possible range due to the rounding.

### Maximum Gradient:
- The maximum rise occurs when the rise is closest to 8.5 meters (since it's rounded to the nearest meter).
- The minimum horizontal distance occurs when it is closest to 115 meters (since it's rounded to the nearest 10 meters).

Thus, the maximum gradient is:

\[
\text{Maximum Gradient} = \frac{8.5}{115} = 0.073913 = 7.39\%
\]

### Minimum Gradient:
- The minimum rise occurs when the rise is closest to 7.5 meters.
- The maximum horizontal distance occurs when it is closest to 125 meters.

Thus, the minimum gradient is:

\[
\text{Minimum Gradient} = \frac{7.5}{125} = 0.060000 = 6.00\%
\]

### Final Answer:
- **Maximum possible gradient:** \( 7.39\% \)
- **Minimum possible gradient:** \( 6.00\% \)

Both answers are rounded to 3 significant figures.

---

Would you like more details on how rounding affects the calculation, or any other clarification?

Here are 5 related questions:
1. How would the gradient change if the road length were measured more accurately?
2. What if the rise was given to the nearest centimeter instead of meter?
3. How do gradients compare in roads versus mountain trails?
4. Can you calculate the angle of the slope based on the gradient?
5. How does the gradient affect driving or walking on a slope?

**Tip:** When working with rounded numbers, consider how rounding may

Discover how to calculate the maximum and minimum gradient of a road that rises 8 meters over a horizontal distance of 120 meters. Learn how rounding impacts the calculations and explore key mathematical concepts like ratios and gradient calculation. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation