How to Calculate Velocity of a River Using Relative Motion Equations?

[JoshMP]

Homework Statement

1. A boat takes 3 hours to travel 30 km down a river, then 5 hours to return. How fast is the river flowing?

2. Taking a moving sidewalk, without walking, takes 75 seconds to arrive at baggage claim. Walking, not on the moving sidewalk, takes 50 seconds. How long will it take you to travel the same distance if you walk while riding on the moving sidewalk?

Homework Equations

v= v' + V

The Attempt at a Solution

I know the answers, but I cannot for the life of me figure out how to set them up mathematically. I am confused how the formula above (given by Galileo) is used for these problems. Any help would be great.

Thanks a lot,
Josh

 

[Jebus_Chris]

1. You have two parts, downstream and upstream. Going downstream the velocity of the river is in the same direction as the velocity of the boat. Going upstream the velocity of the river opposes the velocity of the boat.

2. Well the velocity of walking on the moving sidewalk is the velocity of walking + the velocity of the moving sidewalk. Use an arbitrary distance, x, and figure out what each velocity is.

 

[JoshMP]

Ergo, the boat travels 10km/hr downstream, and 6 km/hr upstream. It would make sense that the velocity of the river is 2 km/hr, but, again, I don't know how to prove it mathematically.