Steve can kayak at 8 km/h in still water. On the river, Steve and the kayak travel slower upstream due to the current. It takes him 1.5 h for a trip downstream, but
3.25 h for the same distance upstream. Determine the speed of the river’s current.
Let distance be D km, and
the current be C km/h
His speed is 8 km/h in still water.
So his speed upstream is
D/3.25=8-C
and downstream,
D/1.5=8+C
Cross multiply each to get
D = 3.25(8-C)
D=1.5(8+C)
Solve by comparison
1.5(8+C)=3.25(8-C)
Isolate C
4.75C = 8(3.25-1.5)
C=8*1.75/4.75
= 2.9 km/hr approximately
Check that the solution works by substituting the solution into the original equations.
To determine the speed of the river's current, we can create a system of equations based on the given information.
Let's denote the speed of the river's current as c (in km/h).
When Steve is kayaking downstream, the effective speed will be the sum of his speed in still water and the speed of the river's current, so his speed downstream will be 8 + c km/h.
Given that it takes him 1.5 hours to kayak downstream, we have the equation:
Distance = Speed x Time
Distance = (8 + c) x 1.5
Now, when Steve is kayaking upstream, the effective speed will be the difference between his speed in still water and the speed of the river's current, so his speed upstream will be 8 - c km/h.
Given that it takes him 3.25 hours to kayak upstream, we have the equation:
Distance = Speed x Time
Distance = (8 - c) x 3.25
Since the distances traveled in both directions are the same, we can set the two equations equal to each other:
(8 + c) x 1.5 = (8 - c) x 3.25
Now, we can solve this equation to find the value of c, which represents the speed of the river's current.