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

part A: I have been pulling my hair out trying to get this part. I just do not see it...

I tried to do the e and f part but I do not understand it eather.

part E: I put the T(x) in my ti-83 for the Y= and then i set my TBLset and then use the table. I do not understand the answer. On my Table when x=20 my Y1 = 1.6853 not the one mile it is asking. Because when x = 25 my table says Y1 = 1.0983 and that seems like it would be closer to one then the answer my books gives.

part F: And how do you do a Minimum on a non - parabola graph. I keep on trying to get but not sure were to look. The book also says that x= 20 miles for this one to.

Ok so if you take your the derivative and set equal to zero to find the min.

I would

(20-x)/5 + (√9+x²)/12 = 0

(20-x)/5 = -(√9+x²)/12

12(20-x) = 5(-3-x)

240 - 12x = -15 + -5x

255 = 7x

36.4286 = x

I am still not getting the 20 miles the books is getting... am i rigtht or is the book?

But when you put it in the table on my TI-83 you get x = 36.4286 and your Y1 = -.2397

Just To Let Everyone Know... I Reworked This Problem This Weekend And I Got It...

Thanks for the update Rob,

Sorry there were not more responses.

BTW, try to edit your initial posts rather than reply to your own thread. Often helpers will only scan the boards for posts that have 0 replies. Unfortunately there is not yet a solution for marking threads solved or as yet unsolved. If any vbulletin buffs know of a solution for this it would be much appreciated.

All the best and better luck in the future