Problem: The current in a river is flowing steadily at 3 miles per hour. A motor boat which travels at a constant rate in still water goes downstream 4 miles and then returns to its starting point. The trip takes one hour, excluding the time spent in turning the boat around. The ratio of the downstream to the upstream rate is .
Answer Choices:
A. 4:3
B. 3:2
C. 5:3
D. 2:1
E. 5:2
Solution:
Let v= the boat's speed in still water in miles per hour. Then 1=v+34​+v−34​ ∴v2−9=4(v−3)+4(v+3)∴v2−8v−9=0,(v−9)(v+1)=0∴v=9 Speed upstream Speed downstream ​=v−3v+3​=612​=12​. The ratio is 2:1.