Question 1029944
It takes longer one way than the other
way because there is a current
Let {{{ 100 }}} = the distance between A and B.
The units do not matter, since no units
of distance are specified
Let {{{ c }}} = the speed of the current in units of 1/1 units/hr
Let {{{ s }}} = the speed of the boat with no current in units of 1/1 units/hr 
Note that 1 unit of distance is 1/100 of the distance AB
Let {{{ t }}} = time in hrs for raft floating with
the current to travel between A and B
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The motorboat going with the current:
(1) {{{ 100 = ( s + c )*32 }}}
The motorboat going against the current:
(2) {{{ 100 = ( s - c )*48 }}}
The raft drifting WITH the current:
(3) {{{ 100 = c*t }}}
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There are 3 equations and 3 unknowns, 
so it's should be solvable
(1) {{{ 100 = 32s + 32c }}}
(2) {{{ 100 = 48s - 48c }}}
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Divide both sides of (1) by {{{2}}}
(1) {{{ 50 = 16s + 16c }}}
Multiply both sides of (1) by {{{ 3 }}}
(1) {{{ 150 = 48s + 48c }}}
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Add (1) and (2)
(1) {{{ 150 = 48s + 48c }}}
(2) {{{ 100 = 48s - 48c }}}
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{{{ 250 = 96s }}}
{{{ s = 2.6042 }}} units/hr
and
(1) {{{ 50 = 16s + 16c }}}
(1) {{{ 25 = 8s + 8c }}}
(1) {{{ 25 = 8*2.6042 + 8c }}}
(1) {{{ 25 = 20.8333 + 8c }}}
(1) {{{ 8c = 4.1667 }}}
(1) {{{ c = .5208333 }}} units/hr
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The raft drifting WITH the current:
(3) {{{ 100 = c*t }}}
(3) {{{ 100 = .5208333*t }}}
(3) {{{ t = 100*1.92 }}}
(3) {{{ t = 192 }}}
The unpowered raft would take 192 hrs
to floor with the current between A and B
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check the answer:
(1) {{{ 100 = ( s + c )*32 }}}
(1) {{{ 100 = ( 2.6042 + .5208333 )*32 }}}
(1) {{{ 100 = 3.1250333*32 }}}
(1) {{{ 100 = 100.00107 }}}
( error due to rounding off )
(2) {{{ 100 = ( s - c )*48 }}}
(2) {{{ 100 = ( 2.6042 - .5208333 )*48 }}}
(2) {{{ 100 = 2.0833667*48 }}}
(2) {{{ 100 = 100.00160 }}}
( error due to rounding off )
(3) {{{ 100 = c*t }}}
(3) {{{ 100 = .5208333*192 }}}
(3) {{{ 100 = 99.9999936 }}}
( error due to rounding off )
OK