Question

A boat travel 4 miles upstream with a current of 5 miles per hour. It takes 40 mminutes longer to go upstream. How fast does the boat go downstream

Answer 1

They probably expect you to assume that the boat is using the same power to go through the water in both directions.

Let V be the boat speed relative to the water in both directions. Relative to the shore, its speed is V+5 going downstream and V-5 going upstream.

Let T be the time that it takes to go downstream, in hours. It take T + 2/3 to go upstream. You can write two equations in the two unknowns, V and T.

4 = (V+5) T
4 = (V-5)(T + 2/3)

4 = (V-5)[4/(V+5) + (2/3)]
4(V+5) = 4(V-5) + (2/3)(V^2-25)
40 = (2/3)(V^2-25)
V^2-25 = 60
V^2 = 85
V = 9.22 mph.
Downstream speed = 14.22 mph
Upstream speed = 4.22 mph
Dowstream travel time = 4/14.22
= 0.281 hrs = 16.9 minutes
Upstream travel time = 4/4.22 = 0.948 hr = 56.9 min