A canoe took 4 hours to travel 18 km with the current On the

A canoe took 4 hours to travel 18 km with the current. On the return trip, the canoe took 6 hours to travel the same distance against the current. When the canoe travels with the current it travels faster than normal. How fast does the canoe travel with the current? One decimal accuracy.

Solution

canoe speed =x km
current speed =y km
against current 6 hours
with current 4 hours

Distance against 18 miles distance with 18 km
t=d/r against current -
18.00 / ( x - y )= 6.00
6.00 ( x - y ) = 4.00
6.00 x - 6.00 y = 18.00 ....................1

18.00 / ( x + y )= 4.00
4.00 ( x + y ) = 18.00
4.00 x + 4.00 y = 18.00 ...............2
Multiply (1) by 4.00
Multiply (2) by 6.00
we get
24.00 x + -24.00 y = 72.00
24.00 x + 24.00 y = 108.00
48.00 x = 180.00
/ 48.00
x = 3.75 km/h

plug value of x in (1) y
6.00 x -6.00 y = 18.00
22.50 -6.00 -22.50 = 18.00
-6.00 y = 18.00
-6.00 y = -4.50 km/h
y = 0.75
canoe speed 3.75 km/h
current speed 0.75 km/h

With current speed = 3.75+0.75 = 4.5 km/h