Time Required to Go from an Island to a Town

Time Required to Go from an Island to a Town. An island is 3 miles from the nearest point P on a straight shoreline. A town is located 20 miles down the shore from P.

(a) A person has a boat that averages 12 miles per hour and the same person can run 5 miles per hour. Express the time T that is takes to go from the island to town, as a function of x, were x is the distance from P to where the person lands the boat. Give the domain.

(b) How long will it take to travel from the island to town if you land the boat 8 miles from P?

(c) How long will it take if you land the boat 12 miles from P?

(d) Graph the function T=T (x).

(e) Create A TABLE with TBLstart = 0 and (increment sign,

Triangle symbol) Tbl = 1. To the nearest mile, determine which value of x results in the least time.

(f) Using MINIMUM, what value of x results in the least time?

(g) The least time occurs by heading directly to town from the island. Explain why this solution makes sense.

Answers

a) T (x) = (20-x)/5 + (√9+x^2)/12 Domain: {x ! 0 (< or =) x (< or =) 20}

b) 3.1 hours

c) 2.6 hours

d) Graph of T (x) = (20-x)/5 + (√9+x^2)/12

e) x = 20 miles

f) x = 20 miles

How do you do a increment sign, Triangle symbol in word?

I have no idea how to do this problem. part a, e, and f