SOLUTION: A pontoon boat moves 6 km/h in still water. It travels 30 km upriver and 30 km downriver in total time of 18 hrs. What is the speed of the current?

Question 318787: A pontoon boat moves 6 km/h in still water. It travels 30 km upriver and 30 km downriver in total time of 18 hrs. What is the speed of the current?
Found 2 solutions by CharlesG2, Fombitz:
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
A pontoon boat moves 6 km/h in still water. It travels 30 km upriver and 30 km downriver in total time of 18 hrs. What is the speed of the current?
6 km/h in still water
30 km upriver (against the current)
30 km downriver (with the current)
total time 18 hrs
let x = speed of boat = 6 km/h
let y = speed of the current
let x + y = speed of boat plus the speed of the current (downriver)
(current speeds up boat)
x + y = 6 + y
let x - y = speed of boat minus the speed of the current (upriver)
(current slows down boat)
x - y = 6 - y
D distance = R rate * T time
30 = (6 + y)T = 6T + yT --> T = 30/(6 + y)
30 = (6 - y)(18 - T) = 108 - 6T - 18y + yT (used FOIL)
6T + yT = 108 - 6T - 18y + yT
6T = 108 - 6T - 18y
12T = 108 - 18y
12T + 18y = 108
12 * 30/(6 + y) + 18y = 108
12 * 30 + 18y(6 + y) = 108(6 + y)
360 + 108y + 18y^2 = 648 + 108y
360 + 18y^2 = 648
18y^2 = 288
y^2 = 16
y = 4 km/h = speed of the current
D distance = R rate * T time
downriver --> 30 = (6 + y)T
30 = (6 + 4)T
30 = 10T
3 = T
upriver --> 30 = (6 - y)(18 - T)
30 = (6 - 4)(18 - 3)
30 = 2 * 15
30 = 30
so speed of current is 4km/h, they took 3 hours to go downriver and 15 hours to go upriver

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Rate*Time=Distance
.
.
.
1. <--- Against the current
2. <--- With the current
3. <--- Total time
From eq. 1,

From eq. 2,

Then substitute into eq. 3,

km/h
RELATED QUESTIONS
A barge moves 6km/h in still water. It travels 51 km upriver and 51 km downriver in a... (answered by sheldonxu)
Please help... A boat moves 7 kph in still water. It travels 445 km upriver and 45 km... (answered by checkley77)
can you solve? A boat moves 7kph in still water. It ravels 45 km upriver and 45 km... (answered by checkley77)
A boat moves 28 km/h in still water. It travels 80 km upstream and 80 km downstream in a... (answered by mananth)
The current in a stream moves at a speed of 5 km/h. A boat travels 39 km upstream and 39... (answered by Alan3354)
The current in a stream moves at a speed of 3km/h. A boat travels 40 km upstream and 40... (answered by josmiceli)
The speed of a boat in still water is 9 km/h. The boat travels 72 km upstream and 72 km... (answered by ikleyn)
The speed of a boat in still water is 8 km/h. It travels 60 km upstream and 60 km... (answered by mananth,ankor@dixie-net.com,Alan3354)
A tourist boat makes trips both upriver and downriver from its mooring. The downriver... (answered by josgarithmetic,josmiceli,MathTherapy)