Question

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?

Answer 1

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`