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#