How do you work this out?
Going downstream a tugboat averages 17 kph. Coming back upstream its average speed is only 6 kph. How fast does the current flow? How fast is the tugboat going?
let the speed of the tugboat in still water be x km/h
let the speed of the current be y km/h
going downstream, the speed would be the sum of the two, while against the current we subtract them,
then x+y = 17 and
x-y = 6
add them
2x = 23
x = 11.5 and y = 17-11.5 = 5.5
so the tugboat's speed is 11.5 km'h
and the current flows at 5.5 km/h
then y =
Downstream Upstream Distance=rate x time
-rate: 1 hour -rate: 1 hour
-time: x+y -time: x-y
-distance: 17km -distance: 6km
System of equations: x+y=17 2x=23 Plug in 11.5 for x x+y=17(rewrite one of the equations:either is fine)
x-y=6 x=11.5km/h in one of the 11.5+y=17(plug in 11.5 for x)
equations(x+y=17 -11.5 -11.5(subtract 11.5 from each side to cancel it out
or x-y=6) y=17-11.5(subtract 11.5 from 17)
y=5.5km/h(get 5.5km/h for final answer)
The current flows 5.5 km/h
The tugboat moves 17 km/h
To determine the speed of the current and the speed of the tugboat, we can use the concept of relative velocity.
Let's assume the speed of the current is represented by 'c' km/h, and the speed of the tugboat is represented by 't' km/h.
When the tugboat is going downstream, its speed gets boosted by the speed of the current. Therefore, its effective speed in still water is 't + c' km/h. Given that the average speed downstream is 17 km/h, we can set up the equation:
t + c = 17 --(1)
When the tugboat is going upstream, its effective speed in still water gets reduced by the speed of the current. Therefore, its effective speed upstream is 't - c' km/h. Given that the average speed upstream is 6 km/h, we can set up the equation:
t - c = 6 --(2)
Now we have a system of two equations with two unknowns (t and c). We can solve this system by either substituting one equation into the other or by adding or subtracting the equations.
Subtracting equation (2) from equation (1), we get:
(t + c) - (t - c) = 17 - 6
2c = 11
c = 11/2
c = 5.5 km/h
So, the speed of the current is 5.5 km/h.
To find the speed of the tugboat, we can substitute the value of c into either equation (1) or (2). Let's use equation (1):
t + 5.5 = 17
t = 17 - 5.5
t = 11.5 km/h
Therefore, the speed of the tugboat is 11.5 km/h.