Question

"a" Adults and "k" students are trying to cross a river with a raft. However the raft can carry only 1 adult at a time, or 2 students, or 1 students. What is the minimum number of trips we need to take to bring everyone across? Express it as a general equation.

Answer 1

Koala Bird has put up a difficult question. I dunno how to do.

Answer 2

x+2k=Answer?
Or;
x+k=Answer?
I really dunno.

Answer 3

If moneybird asks a question, you know it isn't going to be easy

Answer 4

a+k/2 = number of trips.

Answer 5

actually--thats not right, because you need to get the raft back over

Answer 6

a+k = number of trips.

Answer 7

x = trips

2kx(2) = total number of trips

or

ax(2) = total number of trips

or

kx(2) = total numer of trips

or as one equation

kx(2) + 2kx(2) + ax(2) = total number of trips

Answer 8

Here is my attempt at this:
A == Adults
S == Students

Left Right
---- -----
a, k 0A, 0S

a, k-2 0A, 2S -> 2 students take raft from Left to Right
a, k-1 0A, 1S -> 1 student takes raft back to Left
a-1, k-1 1A, 1S -> 1 adult takes raft from Left to Right
a-1, k 1A, 0S -> 1 student takes raft back to Left

a-1, k-2 1A, 2S -+
a-1, k-1 1A, 1S |__ 4 steps to tranfer each adult from Left to Right
a-2, k-1 2A, 1S |
a-2, k 2A, 0S -+

a-2, k-2 2A, 2S
a-2, k-1 2A, 1S
a-3, k-1 3A, 1S
a-3, k 3A, 0S
...

1, k-2 (a-1)A, 2S
1, k-1 (a-1)A, 1S
0, k-1 aA, 1S
0, k aA, 0S --> we get here after 4a trips

0, k-2 aA, 2S -> 2 students take raft from Left to Right
0, k-1 aA, 1S -> 1 student takes raft back to Left

0, k-3 aA, 3S -+
0, k-2 aA, 2S -+-> 2 steps to tranfer each student from Left to Right

0, k-5 aA, 4S
0, k-4 aA, 3S
...

0, 1 aA, (k-1)S
0, 2 aA, (k-2)S --> we get here after 2(k-2) trips

0, 0 aA, kS --> one last trip to get last 2 students across

so total trips = 4a + 2(k-2) + 1 = 4a + 2k -3