How far did Mark row if the entire trip took 4 hours?

Question

Mark can row upstream at 5mph and downstream at 11mph. If Mark starts rowing upstream until he gets tired and then rows downstream to his starting point. 

Answer 1

v = upstream speed = 5

t = upstream rowing time = ?

u = downstream speed = 11

4 - t = downstream rowing time = ?

 

The distances rowed up and down are the same, so

 

vt = u(4 - t)

 

5t = 11(4 - t)

 

Solve the equation above for t, and then get the one-way distance from either 5t or 11(4 - t).

 

t = 44/16 = 2.75 h

 

d = vt = 5(2.75) mi = 13.75 mi

d = 11(4 - t) = 11(4 - 2.75) mi = 13.75 mi

 

Mark rowed 13.75 mi each way, for a total of 27.5 mi.