Question

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?

Answer 1

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 =

Answer 2

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