document.write( "Question 1029944: It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours. How long does it take an unpowered raft to cover this distance? \n" ); document.write( "

Algebra.Com's Answer #644853 by josmiceli(19441) $\"\"$ $\"About$

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It takes longer one way than the other
\n" ); document.write( "way because there is a current
\n" ); document.write( "Let $\"+100+\"$ = the distance between A and B.
\n" ); document.write( "The units do not matter, since no units
\n" ); document.write( "of distance are specified
\n" ); document.write( "Let $\"+c+\"$ = the speed of the current in units of 1/1 units/hr
\n" ); document.write( "Let $\"+s+\"$ = the speed of the boat with no current in units of 1/1 units/hr
\n" ); document.write( "Note that 1 unit of distance is 1/100 of the distance AB
\n" ); document.write( "Let $\"+t+\"$ = time in hrs for raft floating with
\n" ); document.write( "the current to travel between A and B
\n" ); document.write( "--------------------------------------
\n" ); document.write( "The motorboat going with the current:
\n" ); document.write( "(1) $\"+100+=+%28+s+%2B+c+%29%2A32+\"$
\n" ); document.write( "The motorboat going against the current:
\n" ); document.write( "(2) $\"+100+=+%28+s+-+c+%29%2A48+\"$
\n" ); document.write( "The raft drifting WITH the current:
\n" ); document.write( "(3) $\"+100+=+c%2At+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "There are 3 equations and 3 unknowns,
\n" ); document.write( "so it's should be solvable
\n" ); document.write( "(1) $\"+100+=+32s+%2B+32c+\"$
\n" ); document.write( "(2) $\"+100+=+48s+-+48c+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "Divide both sides of (1) by $\"2\"$
\n" ); document.write( "(1) $\"+50+=+16s+%2B+16c+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+3+\"$
\n" ); document.write( "(1) $\"+150+=+48s+%2B+48c+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "Add (1) and (2)
\n" ); document.write( "(1) $\"+150+=+48s+%2B+48c+\"$
\n" ); document.write( "(2) $\"+100+=+48s+-+48c+\"$
\n" ); document.write( "---------------------
\n" ); document.write( " $\"+250+=+96s+\"$
\n" ); document.write( " $\"+s+=+2.6042+\"$ units/hr
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+50+=+16s+%2B+16c+\"$
\n" ); document.write( "(1) $\"+25+=+8s+%2B+8c+\"$
\n" ); document.write( "(1) $\"+25+=+8%2A2.6042+%2B+8c+\"$
\n" ); document.write( "(1) $\"+25+=+20.8333+%2B+8c+\"$
\n" ); document.write( "(1) $\"+8c+=+4.1667+\"$
\n" ); document.write( "(1) $\"+c+=+.5208333+\"$ units/hr
\n" ); document.write( "-------------------------
\n" ); document.write( "The raft drifting WITH the current:
\n" ); document.write( "(3) $\"+100+=+c%2At+\"$
\n" ); document.write( "(3) $\"+100+=+.5208333%2At+\"$
\n" ); document.write( "(3) $\"+t+=+100%2A1.92+\"$
\n" ); document.write( "(3) $\"+t+=+192+\"$
\n" ); document.write( "The unpowered raft would take 192 hrs
\n" ); document.write( "to floor with the current between A and B
\n" ); document.write( "-----------------
\n" ); document.write( "check the answer:
\n" ); document.write( "(1) $\"+100+=+%28+s+%2B+c+%29%2A32+\"$
\n" ); document.write( "(1) $\"+100+=+%28+2.6042+%2B+.5208333+%29%2A32+\"$
\n" ); document.write( "(1) $\"+100+=+3.1250333%2A32+\"$
\n" ); document.write( "(1) $\"+100+=+100.00107+\"$
\n" ); document.write( "( error due to rounding off )
\n" ); document.write( "(2) $\"+100+=+%28+s+-+c+%29%2A48+\"$
\n" ); document.write( "(2) $\"+100+=+%28+2.6042+-+.5208333+%29%2A48+\"$
\n" ); document.write( "(2) $\"+100+=+2.0833667%2A48+\"$
\n" ); document.write( "(2) $\"+100+=+100.00160+\"$
\n" ); document.write( "( error due to rounding off )
\n" ); document.write( "(3) $\"+100+=+c%2At+\"$
\n" ); document.write( "(3) $\"+100+=+.5208333%2A192+\"$
\n" ); document.write( "(3) $\"+100+=+99.9999936+\"$
\n" ); document.write( "( error due to rounding off )
\n" ); document.write( "OK \n" ); document.write( "

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