Word Problem (Boat Trip) Help, PLEASE?

Question

A man who lives in the South Pacific is planning a rowboat trip. His rowboat will hold him plus enough food to last three weeks. By a strange coincidence, several small islands about one week's rowing apart are near the island he lives on. He plans on rowing to the fifth island, which is a large island with grocery stores similar to those on the main island he lives on now. But the four small islands between his island and the other big island have no stores, and he will not be able to buy any food on those islands. So he realizes that he will have to row out to an island, store some food, and return to the main island for more supplies. Show how he could organize his food supplies so he can get to the fifth island. How many weeks will his trip take altogether?

Please show/explain each step!

Thanks!

Answer 1

he rows to the 1st and leaves 1 weeks food and rows home. he repeats th same trip. the third time he goes to the second island and leaves 1 week food and returns to 2nd island for food and returns home. he repeats the double trip to the first island leaving 1 weeks food both times. so on the sixth trip he makes the second island leaving a 2nd weeks food and returns home.now he can leave home and make it to the fifth island restocking food at the second island and arriving at island five 21 weeks later.

Answer 2

1

Answer 3

He can make it from island 2 to island 5 on one boatload (3x). He can get from home to island 2 on 2/3 boatload (2x), so he needs to store 2x on island 2. Two trips to island 1 allows him to stockpile 2 weeks food there. That takes 3 weeks, leaving him on island 1 with 4 weeks food. A round trip to island 2 from island 1 takes another 2 weeks, and the trip home takes 1 week, leaving 1 week's food on island 2 and none on island 1, consuming a total of 6 weeks. Repeating this process takes another 6 weeks, for a total of 12. Now he can make the trip to island 5 in 5 weeks, resupplying at island 2. The total time involved is 17 weeks.

Edit:
Rethinking, after the first 6-week cycle, 3 more trips leaves him on island 1 with 3 weeks food. Another week leaves him at island 2 with 3 weeks food, and 3 more weeks will take him to island 5, with a total time consumed of 7 + 6 = 13 weeks.

Answer 4

This is going to sound complicated, but:
I don't see any information about the distances (other than the 1 week deal. are they all 1 week apart?), speed, or current. Let's assume the following: (you might want to draw this) 1. the island he is leaving (label as a) is inbetween the 2 other islands with stores (label as b and c) and 2. the 4 islands without food (label as d, e, f, and g) and his destination (label as h) in a generally straight line. you would be able to draw lines inbetween d and b, d and c, e and b, e and c, f and c, f and b, g and b, g and c. now we're working with triangles. for a right triangle, the hypotenuse (long line) formula equation is: short line ^2 + short line ^2 = long line^2. draw a line island a to island h. draw a line from h to b and from h to c. draw a line from b to c. You should have several triangles inside a large one.
you might want to write this down too. x^2 = travel time in 1 direction.
My guess, based on the drawing, b to a=1 week, a to c = 1 week, a to d=1 week. triangles abd and acd=(1^2)+(1^2)=x^2. x=1 week b to d and c to d= 1 week. triangles abe and ace = (1^2)+(2^2)=x^2. e to b and e to c = square root of 5 weeks. triangles abf and acf = (1^2)+(3^2)=x^2. x= square root of 10 weeks. triangles abg and acg = (1^2)+(4^2)=x^2. b to g and c to g = square root of 17 weeks.
b to d to b = 2 weeks
b to e to b = 4.47 weeks (c to d to c also) (square root of 5 + square root of 5)
b to f to b = 6.32 weeks
b to g to b = 8.24 weeks
if he gets food then heads for g, that creates another triangle.

my drawing looks like this; g
f
e
d
b a c

my guess is go past d, but not to e. head to b or c, then head to g. square root of 10 is 3.16

beyond this, I don't know what to tell you. I hope this at least gives you something to work with.

Answer 5

It is perhaps best to work this backwards. In order to just get to the 5th island, he should leave the 2nd island with a full boat. His 3 weeks supply in the full boat will just get him to the 5th island.

To do this, he needs to arrive at island 2 with a store of food plus what is in the boat of 3 weeks. He could arrive at island 2 with 2 weeks food after leaving island 1 with a full boat. This means he needs to store 1 week food on island 2. He needs to leave island 1 with a full boat to do this. Since island 1 is one week out, he must stor just 1 week food on island 1. So, all he needs to do is to get 1 week on each island 1 and 2 before the final trip.

He can make a round trip to island 1 and leave 1 week on the island for each trip. To leave 1 week on island 2 he needs to start full, go to island 1, pick up 1 week food, go to island 2 and drop off one week and pick up another week on island 1 on the way back home.

All in all, he needs 3 weeks on island 1 to be able to get 1 week out to island 2. This means three round trips to island 1, a single round trip to island 2 and a one-way trip to island 5.

He spends 6 weeks doing the three round trips to island 1, 4 weeks doing the round trip to island 2, and 5 weeks to go one-way to island 5. This makes 15 weeks of rowing.

And to answer Zackfasho, this is an excellent problem posed in the right place.

Answer 6

First of all, this isn't a math question. There is no miles/speed, distance. Just how long his food will last.I guess he should go dump some food off at the first island and then go back and get more supplies. Really there is no info to go on here. That is the best i can do. Who ever gave this to you to solve is dumb. =D

Answer 7

Complete Boat Building Guide : http://BoatPlans.NaturallyGo.com/?Xin

Answer 8

a million.5(r + c) = 12-->a million.5r + a million.5c = 18-->4(a million.5r + a million.5c = 18) 2(r - c) = 12----->2r - 2c = 24-------->3(2r - 2c = 24) 6r + 6c = seventy two 6r - 6c = seventy two 12r = a hundred and forty four r = 12 fee of the boat 2(r - c) = 12 2(12) - 2c = 12 24 - 2c = 12 12 = 2c c = 6 fee of the present