Solving a Rowing Kinematics Problem: Finding the Rate of the Current

[Omid]

A man who can row 4 miles per hour in still water finds that he can row upstream in 7 and 1/2 hours a distance which requires 2 and 1/2 hours to row downstream. Find the rate of the current.

When I saw the problem at once I had dozens of ideas to solve it but all of them failed.
Can you give me some hints ?

Thanks

 

[Galileo]

The most direct way would be setting up the known equations and solve for them.
You have two unknowns, the speed of the current and the distance travelled.
You also have two linearly independent equations:
-The 'speed*time=distance' equation for going upstream
-The 'speed*time=distance' equation for going downstream

The speed when going upstream/downstream is just the speed of the man minus/plus
the speed of the current.

 

[HallsofIvy]

Let the current be v. Speed upstream is 4-v and the distance rowed in 7 and 1/2 hours is d= (4-v)(15/2). Speed downstream is 4+v and the distance rowed in 2 and 1/2 hours is (4+v)(5/2). Since those distances are the same, set them equal and solve for v.

 

[Omid]

I was making the problem harder and harder by using relative motion and vectors, ... that's why I couldn't solve it.
I must remember to kiss ( Keep It Simple and Straight forward) , as you did here, when solving physics problems.

Thank you very much

 

[HallsofIvy]

You mean it's not "Keep it simple, STUPID"? That's what people always tell ME!

 

[Omid]

You mean it's not "Keep it simple, STUPID"? That's what people always tell ME!