SOLUTION: A tourist boat makes trips both upriver and downriver from its mooring. The downriver trip is 36 km each way and takes 8 hours for the round trip. The upriver destination is 60 km

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Question 1033438: A tourist boat makes trips both upriver and downriver from its mooring. The downriver trip is 36 km each way and takes 8 hours for the round trip. The upriver destination is 60 km away and it takes 10 hours to get there. Find the speed of the boat in still water and the speed of the river.
Found 3 solutions by josgarithmetic, josmiceli, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The description is of two problems. The tourist boat is doing two round trips. This is a data table for the 36 distance trip which is a 72 km round trip. The 60 km, 10 one-way is a separate problem and should be simpler to solve. 
                     speed       time        distance

Going, downriver      r+c        36/(r+c)    36

Return, upriver       r-c        36/(r-c)    36

TOTAL                            8


Basic Rates Rule and sum of times gives 36%2F%28r%2Bc%29%2B36%2F%28r-c%29=8, and you will need the other part of the description to analyze and them form an additional equation. You will have two equations then, and two unknowns of r and c. 

                   RATE      TIME       DISTANCE
GOING (UPRIVER)    r-c       10          60
RETURN             r+c      not needed not given

%28r-c%29%2A10=60


System of equations to solve is system%2836%2F%28r%2Bc%29%2B36%2F%28r-c%29=8%2C10%28r-c%29=60%29.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the boat in still water in km/hr
Let +c+ = the speed of the current in km/hr
Let +t+ = time in hrs for the downriver trip ( going downriver )
+8+-+t+ = time in hrs for the downriver trip ( going back upriver )
---------------------------------
Equation for downriver trip ( going downriver ):
(1) +36+=+%28+s+%2B+c+%29%2At+
Equation for downriver trip ( going upriver ):
(2) +36+=+%28+s+-+c+%29%2A%28+8+-+t+%29+
Equation for the upriver trip, one-way ( going upriver )
(3) +60+=+%28+s+-+c+%29%2A10+
---------------------------
(3) +s+-+c+=+6+
and
(1) +s+%2B+c+=+36%2Ft+
---------------------
Add the equations
+2s+=+36%2Ft+%2B+6+
+s+=+18%2Ft+%2B+3+
and
(3) +s+=+c+%2B+6+
+18%2Ft+%2B+3+=+c+%2B+6+
+c+=+18%2Ft+-+3+
----------------------
(2) +36+=+%28+s+-+c+%29%2A%28+8+-+t+%29+
(2) +36+=+%28+18%2Ft+%2B+3+-+18%2Ft+%2B+3+%29%2A%28+8+-+t+%29+
(2) +36+=+6%2A%28+8+-+t+%29+
(2) +36+=+48+-+6t+
(2) +6t+=+12+
(2) +t+=+2+
and
+s+=+18%2Ft+%2B+3+
+s+=+18%2F2+%2B+3+
+s+=+12+
and
+c+=+18%2Ft+-+3+
+c+=+18%2F2+-+3+
+c+=+6+
-----------------
The speed of the boat in still water is 12 km/hr
The speed of the current is 6 km/hr
------------------------------
check:
(1) +36+=+%28+s+%2B+c+%29%2At+
(1) +36+=+%28+12+%2B+6+%29%2A2+
(1) +36+=+18%2A2+
(1) +36+=+36+
and
(2) +36+=+%28+s+-+c+%29%2A%28+8+-+t+%29+
(2) +36+=+%28+12+-+6+%29%2A%28+8+-+2+%29+
(2) +36+=+6%2A6+
(2) +36+=+36+
and
(3) +60+=+%28+s+-+c+%29%2A10+
(3) +60+=+%28+12+-+6+%29%2A10+
(3) +60+=+6%2A10+
(3) +60+=+60+
OK

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A tourist boat makes trips both upriver and downriver from its mooring. The downriver trip is 36 km each way and takes 8 hours for the round trip. The upriver destination is 60 km away and it takes 10 hours to get there. Find the speed of the boat in still water and the speed of the river.
Let speed of boat in still water, be S, and speed of river, R

Since it takes 8 hours for round-trip, we get: 

36%2F%28S+%2B+R%29+%2B+36%2F%28S+-+R%29+=+8 ------- eq (i)

Also, S+-+R+=+60%2F10______S – R = 6_____S = 6 + R ------- eq (ii)

36%2F%286+%2B+R+%2B+R%29+%2B+36%2F%286+%2B+R+-+R%29+=+8 ------- Substituting 6 + R for S in eq (i)

36%2F%286+%2B+2R%29+%2B+36%2F6+=+8

36%2F%286+%2B+2R%29+%2B+6+=+8

36%2F%286+%2B+2R%29+=+8+-+6 

36%2F%286+%2B+2R%29+=+2

2(6 + 2R) = 36 -------- Cross-multiplying

6+%2B+2R+=+36%2F2 ------ Dividing by 2

6 + 2R = 18

2R = 18 – 6

2R = 12

R, or speed of river = 12%2F2, or highlight_green%28matrix%281%2C2%2C+6%2C+%22km%2Fh%22%29%29

S = 6 + 6 -------- Substituting 6 for R in eq (ii)

S, or speed of boat, in still water = highlight_green%28matrix%281%2C2%2C+12%2C+%22km%2Fh%22%29%29