posted by Kim on .
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
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