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

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)   (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 , 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

System of equations to solve is .
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the speed of the boat in still water in km/hr
Let = the speed of the current in km/hr
Let = time in hrs for the downriver trip ( going downriver )
= time in hrs for the downriver trip ( going back upriver )
---------------------------------
Equation for downriver trip ( going downriver ):
(1)
Equation for downriver trip ( going upriver ):
(2)
Equation for the upriver trip, one-way ( going upriver )
(3)
---------------------------
(3)
and
(1)
---------------------
Add the equations

and
(3)

----------------------
(2)
(2)
(2)
(2)
(2)
(2)
and

and

-----------------
The speed of the boat in still water is 12 km/hr
The speed of the current is 6 km/hr
------------------------------
check:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
and
(3)
(3)
(3)
(3)
OK
Answer by MathTherapy(10552)   (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:
------- eq (i)
Also, ______S � R = 6_____S = 6 + R ------- eq (ii)
------- Substituting 6 + R for S in eq (i)

2(6 + 2R) = 36 -------- Cross-multiplying
------ Dividing by 2
6 + 2R = 18
2R = 18 � 6
2R = 12
R, or speed of river = , or
S = 6 + 6 -------- Substituting 6 for R in eq (ii)
S, or speed of boat, in still water =
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