# A boat takes 3 hours to travel 30 km down a river, then 5 hours to return. How fast is the river flowing?

• The average time of the trip, which cancels out the current, is 4 hours, so the boat's motor is pushing it at 7.5 km/h. You can figure out the rest.

• Here's what we know:

distance = rate X time. Let s = the speed of the river, r = the speed of the boat relative to the river. Then

30 Km = (r + s) X 3 [The speed down-river is the boat's speed plus the river's speed]

and

30 Km = (r - s) X 5 [The speed up-river is the boat's speed minus the river's speed]

Since 30 Km = 30 Km, (r + s) X 3 = (r - s) X 5

Solving for s:

3r + 3s = 5r - 5s

8s = 2r

s = r/4

Putting this back in the first equation,

30 Km = (r + r/4) X 3.

Solving for r:

15r/4 = 30 Km

So r = 8 Km/hr (speed of the boat) and

s = 2 Km/hr (speed of the river)

Source(s): high school algebra
• 3x30 = 90km.

90/5=18km speed while returning.

30-18=12

River helps boat while going and slows it down while returning. Therefore, 12/2=6km change is the on boat's speed. Therefore, river's flowing speed is 6km.

• Fast enough to slow it by 2 hrs