Problema Solution
A boat takes 1.5 hour to go 12 mile upstream against the current. It can go 24 mile downstream with the current in the same amount of time. Find the speed of the current and the speed of the boat in still water.
Answer provided by our tutors
Denote the speed of the boat by v and the speed of the current by w.
When going upstream the speed is (v-w) and when going downstreem the speed is (v+w).
Using the equation speed = distance/time:
12 miles upstream take 1.5 hours, so v-w=12/1.5=24/3=8 m/h
24 miles downstream take 1.5 hours as well, so v+w=24/1.5=48/3=18 m/h
We have two equations: v-w=8, v+w=18.
Add them: v-w+v+w=8+18 ==> 2v=26 ==> v=13
Plug in one of the equations to get w: 13+w=18 ==> w=15
The speed of the current is 5 miles per hour.
The speed of the boat (in still water) is 13 miles/hour.