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

4 Answers

• 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