A river boat travels from port A to port B, a distance of 15.0 km downstream, in 1 hour 40 minutes. The return journey takes 2 hours 30 minutes. Calculate: (a) the boat speed relative to the water? (b) the speed of the river?

1 Answer
Apr 16, 2018

A.
(0.025km)/min=0.41666....m/s
B.
(0.125km)/(min)=2.08333....m/s

Explanation:

Speed = (Deltax)/(Deltat)
Downstream:
Deltax=15km
Deltat=1h40min=100min
Speed=(15km)/(100min)
Speed=(0.15km)/min

Upstream:
Deltax=15km
Deltat=2h30min=150min
Speed=(15km)/(150min)
Speed=(0.1km)/min

The boat's speed relative to the water is equal to the average of its two speeds, so
(((0.15km)/min)+((0.1km)/min))/2, which equals
(0.125km)/(min)

The river's speed is the difference between the boat's relative speed and its actual speed, so |(0.15km)/min-(0.125km)/(min)|, which equals
(0.025km)/min

Now, using dimensional analysis, you can convert (km)/min to m/sec using a factor of 1000/60 (If you need help on this feel free to ask), so the river's speed is
(0.025km)/min*1000/60=0.41666....m/s
and the boat's speed is
(0.125km)/(min)*1000/60=2.08333....m/s