Question

Smithville has 8 inches of snow, and it is melting at a rate of 7/10 inch per day. Kansas City has 6 inches of snow, and it is melting at a rate of 1/5 inch per day. Which of the following equations represents the remaining snow depth (S) in Smithville (S_s) and Kansas City (S_k) as a function of time (t) in days?

A) S_s(t) = 8 - (7/10)t
S_k(t) = 6 - (1/5)t
B) S_s(t) = 8 - (1/5)t
S_k(t) = 6 - (7/10)t
C) S_s(t) = 8 - (1/10)t
S_k(t) = 6 - (2/5)t
D) S_s(t) = 8 - (2/5)t
S_k(t) = 6 - (1/10)t

Answer 1

The correct equations representing the remaining snow depth for Smithville and Kansas City as a function of time are S_s(t) = 8 - (7/10)t for Smithville and S_k(t) = 6 - (1/5)t for Kansas City, corresponding to Option A.

Step-by-step explanation:

The remaining snow depth (S) in Smithville (S_s) and Kansas City (S_k) as a function of time (t) in days is given by two linear equations. Considering the rates of melting provided, the equations for Smithville and Kansas City can be formed. For Smithville, the initial snow depth is 8 inches and it melts at a rate of 7/10 inch per day, which gives us the equation S_s(t) = 8 - (7/10)t. For Kansas City, the initial snow depth is 6 inches and it melts at a rate of 1/5 inch per day, resulting in the equation S_k(t) = 6 - (1/5)t. Therefore, the correct equations that represent the remaining snow depth for Smithville and Kansas City as a function of time are Option A: S_s(t) = 8 - (7/10)t and S_k(t) = 6 - (1/5)t.