could you answer this???

Question

Your party consits of six adults and four children. While on a hike, you come upon a river which you will need to cross in order to continue on your hiking trail. At the edge of the river one of your friends find a small boat. It can accommodate only one adult at a time. Or it can accommodate at most two children. It will not hold one adult and one child at the same time. Everyone is capable of rowing the boat. So the question is how many one-way trips does it take for everyone to reach the other side? if you can explain it by an equation?

Answer 1

I assume you always need someone to row the boat. It wouldn't make sense to send an adult, since they would have to row the boat back, so definitely start with two children:

It takes 4 trips to get an adult over:
AAAAAAcc --> cc --> cc
AAAAAAccc <-- c <-- c
AAAAAccc --> A --> Ac
AAAAAcccc <-- c <-- A

You can repeat this for the next adult:
AAAAAcc --> cc --> Acc
AAAAAccc <-- c <-- Ac
AAAAccc --> A --> AAc
AAAAcccc <-- c <-- AA

And again until you have all the adults (total trips so far 6 adults x 4 trips per adult = 24 trips):

To get a child over takes a couple one way trips: (total 26)
cc --> cc --> AAAAAAcc
ccc <-- c <-- AAAAAAc

To get the next child over takes two more: (total 28)
c --> cc --> AAAAAAccc
cc <-- c <-- AAAAAAcc

The last two can make a single trip: (total 29)
--> cc --> AAAAAAcccc

So it takes 6 x 4 + 2 x 2 + 1 trips:

Total one way trips = 29