At the end of a snow storm, Audrey saw there was a lot of snow on her front lawn. The temperature increased and the snow began t
o melt at a steady rate. There was a depth of 10 inches of snow on the lawn when the storm ended and then it started melting at a rate of 2 inches per hour. Write an equation for S, in terms of t, representing the depth of snow on Audreys lawn, in inches, t hours after the snow stopped falling.
At the end of a snow storm, Audrey saw there was a lot of snow on her front lawn. The temperature increased and the snow began to melt at a steady rate. There was a depth of 10 inches of snow on the lawn when the storm ended and then it started melting at a rate of 2 inches per hour. Write an equation for S, in terms of t, representing the depth of snow on Audreys lawn, in inches, t hours after the snow stopped falling.
2 inches = 1 hour
10 inches = x hour
2x = 10
x = 10/2
x = 5
Creating an equation
S ∝ t
S = kt
k = s/t
k = 2/1
k = 2
The equation for S, in terms of t, representing the depth of snow on Audreys lawn, in inches, t hours after the snow stopped falling is
Just substitute the first equation into the second and solve for x: <span><span>32</span>x=−<span>12</span>x+4⟹2x=4⟹x=2</span><span>Now, since y = 3/2 * x, we have y = 3 and we are done.</span>
