Question

1. you are travelling home on a bike and have a choice of two routes. the first route has an elevation of 225m over the horizontal distance of 1000m. the second route has an elevation of 230m over the horizontal distance of 975m. find the slope of both routes and decide which route you would want to take home and justify your answer. keep all decimal places.

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{\text{vertical change}}{\text{horizontal change}}$.

Step2: Calculate slope of first route

For the first route, the vertical change (elevation) is $225$m and the horizontal change is $975$m. So the slope $m_1=\frac{225}{975}\approx 0.23$.

Step3: Calculate slope of second route

For the second route, the vertical change (elevation) is $230$m and the horizontal change is $1000$m. So the slope $m_2=\frac{230}{1000}= 0.23$.

Step4: Compare slopes and make a decision

Since $m_1\approx0.23$ and $m_2 = 0.23$, the slopes are approximately equal. However, the first - route has a shorter horizontal distance. So, it might be a better choice as it will likely take less time to cover the horizontal part of the journey.

Answer:

The slope of the first route is approximately $0.23$. The slope of the second route is $0.23$. The first route might be a better choice because it has a shorter horizontal distance while having a similar slope.