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**lancelot854** The tide removes the sand from a beach at a rate modeled by the function R, given by$\displaystyle R(t) = 2+5sin\frac{4*pi*t}{25}$. A pumping station adds sand to the beach at a rate modeled by the function S, given by $\displaystyle S(t)=(15t)/(1+3t)$.

Both R(t) and S(t) have units of cubic yards per hour and t is measured in hours for $\displaystyle 0=<t=<6$. At time $\displaystyle t=0$, the beach contains 2500 cubic yards of sand.

How much sand will the tide remove from the beach during this 6 hour period. Indicate units of measure. Write an expression for the total number of cubic yards of sand on the beach at time t.