### Solution to Episode Two: The Trip Across Styx

A)What is the function that represents the velocity of the boat?

Because Charon keeps his boat at a constant speed of 6 m/s, but the boat causes it to speed up by another 4 m/s every other second, the equation is v(t)=4t+6

B)Given the time interval of the trip, how far will the boat travel before letting the prince off?

It takes the ferryman 29 seconds to cross the river, so the time interval of the entire trip would be from t=0 to t=29. Using the fundamental theorem, we find that the distance travelled is 1856 meters.

C)What will his final fare at the end of the trip be?

Because Charon charges 1 gold coins for every 4 meters, by taking the total distance and dividing it by 4, it give the total cost of the trip.

1856/4=464 gold coins

Because Charon keeps his boat at a constant speed of 6 m/s, but the boat causes it to speed up by another 4 m/s every other second, the equation is v(t)=4t+6

B)Given the time interval of the trip, how far will the boat travel before letting the prince off?

It takes the ferryman 29 seconds to cross the river, so the time interval of the entire trip would be from t=0 to t=29. Using the fundamental theorem, we find that the distance travelled is 1856 meters.

C)What will his final fare at the end of the trip be?

Because Charon charges 1 gold coins for every 4 meters, by taking the total distance and dividing it by 4, it give the total cost of the trip.

1856/4=464 gold coins