What Are the Solutions to These River Current Boat Problems?

[NoPhysicsGenius]

[SOLVED] Boat in the river problems

Homework Statement

(a.) A boat took 1 hour 50 minutes to go 55 miles downstream and 3 hours 40 minutes to return. Find the rate of the current.

(b.) A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream. The speed of the boat is 15 mi/h greater than the speed of the current. Find the speed of the current.

(c.) A boat travels 12 miles downstream in 1.5 hours. On the return trip the boat travels the same distance upstream in 2 hours. Find the rate of the boat in still water and the rate of the current.

Homework Equations

distance = rate * time

The Attempt at a Solution

I can't figure out how to solve any of these. Could you at least help me to set them up correctly? Thank you.

 

[member 553083]

(a.) Let x be the rate of the current. We have 55/x + (55/x -15) = 5.5 + 6.667 55/x = 11.167 x = 5 mph (b.) Let y be the speed of the current. We have 60/(y+15) + 36/(y-15) = 4 + 3 96/y = 7 y = 13.7 mph (c.) Let z be the rate of the boat in still water and a be the rate of the current.We have 12/z + 12/(z+a) = 1.5 + 2 24/z = 3.5 z = 6.86 mph and 12/(z-a) + 12/z = 2 + 1.5 24/z = 3.5 a = 3.14 mph