A dehydrated person containing 5L of blood in their body has been found to have a concentration of 120 mEq/L(milliequivalents per litre), well below the normal of 135 mEq/L. To restore the person's electrolites, a saline solution containing 150 mEq/L is infused into their body at a rate of 0.125L/hour . At any time, The body will use 1% of the sodium present in the blood.

a) Set up and solve an initial value problem that models the amount S of sodium in the person's blood.

b) Determine how long it will take the person to reach the normal sodium concentration.