Distance, Rate, Time Problem

Question

Two friends can paddle a canoe at a rate of 6 km/h in still water. It takes them 1 h to paddle 2 km up a river and back again. Find the speed of the current.

 

 

I get the general sense of the problem, but why is it 6+x and 6-x and not x+6 and x-6?

Answer 1

6 + x represents the speed of the people when they're traveling with the direction current. That's because this is they have their paddling speed of 6 km/h, and then the current, which is x, is helping to push them more and make them go faster. That's why the two speeds add up.

 

For 6 - x, imagine this. They have their speed, but they're slowed down a bit by the current. 6 - x is a term because the current is taking away from their paddling speed. It is not x - 6, because x is the speed of the current, so x - 6 would mean that the current is being slowed down by them, which is not the case.