Boat rate of change problem

Question

A boat travels with the current at 21 km/hr and travels against the current at 13 km/hr. The speed of the boat in still water is v km/hr. What is the value of v?

Answer 1

When you think of the speed (rate) of a boat and the current, we first need to understand that a boat travelling upstream, against the current, will travel slower than a boat travelling downstream, with the current.

So if v is the speed of the boat in still water and c is the current

v+c = downstream rate

v-c = upstream rate

Per the problem

v+c=21

v-c=13

We can solve this system of equations using elimination by adding the two equations together.

v+c=21

v-c=13

2v = 34

divide both sides by 2

v = 17 km/hr.