Word problem - pre calc

Question

If An island is 2.8 kilometers from the nearest point, P, on a straight shoreline. A town is 6.3 kilometers down the shore from Point P. If a person can row a boat at an average speed of 4.1 kilometers per hour and the same person can walk 4.6 kilometers per hour, build a mode that expresses the time, T, that it takes to go from the island to the town as a function of the distance, X, from, P, where the person lands the boat.

 

T(x) =

Answer 1

The key to solving problems of this type is to draw a picture.  When that is done, it can be seen that the points p, x, and the island form a right triangle with the hypothesis representing the distance between the island and X.

 

So the distance traveled by boat can be found using the pythogorean theorem.

 

d_boat =√ (x² +2.8²)    So the time traveled by boat is 

 

t_^boat = d_boat/4.1km/hr = 1/4.1 * √ (x² +2.8²)

 

The distance given by boat is found by simpy subtracting x from 6.3 miles. 

 

d_walk = 6.3-x

t_walk = d_walk/4.6km/hr = 1/4.6 * (6.3 - x).

 

So the total time t_total = t_walk + t_boat 

 

= 1/4.6 * (6.3 - x) + 1/4.1 * √ (x² +2.8²)