SOLUTION: I need some help in solving this problem. The current ina stream moves at a speed of 2 km/h. A boat travel 27 km upstream and 27 km downstream in a total of 17 hours. What is the

Click here to see ALL problems on Matrices-and-determiminant

Question 329422: I need some help in solving this problem. The current ina stream moves at a speed of 2 km/h. A boat travel 27 km upstream and 27 km downstream in a total of 17 hours. What is the speed of the boat in still water?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The current in a stream moves at a speed of 2 km/h.
A boat travel 27 km upstream and 27 km downstream in a total of 17 hours.
What is the speed of the boat in still water?
---
Upstream DATA:
distance = 27 km ; rate = (x-2) km/h ; time = d/r = 27/(x-2) hrs.
---------------------------
Downstream DATA:
distance = 27 km ; rate = (x+2) km/h ; time = 27/(x+2)
----------------------------
Equation:
time up + time down = 17
27/(x-2) + 27(x+2) = 17 hrs
-------------------------------
Multiply thru by (x-2)(x+2)
---
27(x+2) + 27(x-2) = 17(x^2-4)
54x = 17x^2 - 68x
---
17x^2 - 122x = 0
x(17x-122) = 0
Positive solution:
x = 122/17 = 7.1765 km/h (speed of the boat in still water)
==============================================================
Cheers,
Stan H.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the speed of the boat in still water. Then represents the upstream speed and represents the downstream speed. Let represent the elapsed time for the upstream trip, then represents the elapsed time for the downstream trip.

Just solve for .

John

My calculator said it, I believe it, that settles it