Driving down Bald Mountain in Wyoming, Bob dean finds that he descends 1600 feet in elevation by the time he is 2.5 miles (horizontally) away from the high point on the mountain road. Find the slope of his descent (Hint: 1 mile = 5280 feet)
After converting the miles to feet I got 1600/13200. After that I found a number in common of 400 which gave me my answer of 4/33 as the slope.
I feel like I did this wrong and when I go to look at the examples in my book it doesn't show any for this type of problem. So if you could help me I would really appreciate it.
Well, Bob certainly had quite a downhill ride! Let's double-check your calculations to see if you're on the right track.
First, let's convert the 2.5 miles to feet, as you correctly mentioned. Since 1 mile = 5280 feet, 2.5 miles would be 2.5 * 5280 = 13,200 feet.
Now, to find the slope, we divide the change in elevation (1600 feet) by the horizontal distance traveled (13,200 feet). So, the slope would be:
1600 feet / 13,200 feet = 0.1212121212...
This is a recurring decimal, but let's round it to three decimal places, which gives us approximately 0.121.
So, the slope of Bob's descent is approximately 0.121.
To find the slope of the descent, you first need to determine the change in elevation compared to the change in horizontal distance. Since you correctly converted the 2.5 miles to 13200 feet, you are on the right track.
The change in elevation is given as 1600 feet, and the change in horizontal distance is 13200 feet. This means that for every 13200 feet horizontally, the road descends 1600 feet.
To find the slope, you divide the change in elevation by the change in distance:
Slope = change in elevation / change in distance
Slope = 1600 feet / 13200 feet
Simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 400:
Slope = (1600 feet / 400) / (13200 feet / 400)
Slope = 4 / 33
So, the slope of the descent is 4/33. You did it correctly!
To find the slope of Bob's descent, you need to divide the change in elevation by the change in horizontal distance.
First, let's convert the 2.5 miles (horizontally) into feet using the conversion factor given: 1 mile = 5280 feet.
So, 2.5 miles = 2.5 * 5280 feet = 13,200 feet.
Now we can calculate the slope by dividing the change in elevation, which is 1600 feet, by the change in horizontal distance, which is 13,200 feet.
Slope = Change in elevation / Change in horizontal distance = 1600 feet / 13,200 feet.
To simplify the fraction, we can divide both the numerator and denominator by a common factor, like 400.
1600 / 400 = 4
13200 / 400 = 33
Therefore, the slope of Bob's descent is 4/33.
You did it correctly by simplifying the fraction and obtaining a slope of 4/33. Well done!
looks good to me.
slope = ∆y/∆x = 1600/13200 = 4/33