If a car is traveling downhill at 45 miles per hour on dry pavement, then the braking distance B is
B = 45/(0.4+m), where m<0 is the slope of the road.
Find the slope of the road if the braking distance is 125 feet.
125 = 45/(0.4+m)
0.4+m = 45/125
m = 45/125 - 0.4
m = -0.04
To find the slope of the road, we can use the given equation and solve for the slope value when the braking distance is 125 feet.
The equation for the braking distance B is:
B = 45 / (0.4 + m)
Given that B = 125 feet, we can substitute this value into the equation:
125 = 45 / (0.4 + m)
To solve for the slope m, we will rearrange the equation:
125(0.4 + m) = 45
Now, let's simplify the equation:
50 + 125m = 45
Next, subtract 50 from both sides of the equation:
125m = 45 - 50
125m = -5
Finally, divide both sides of the equation by 125 to isolate m:
m = -5 / 125
m = -0.04
Therefore, the slope of the road is -0.04 or -4%.