M10-04

Official Solution:

A steamer takes 4 hours and 30 minutes to travel from Town A to Town B when traveling upstream against the current. However, it only takes the steamer 3 hours to travel from Town B to Town A when traveling downstream with the current. Assuming the current flows at a constant speed, how long will it take a raft, floating downstream at the speed of the current, to travel from Town B to Town A ?

A. 10 hours
B. 12 hours
C. 15 hours
D. 18 hours
E. 20 hours


Assume the speed of the steamer in still water is \(s\) and the speed of the current to is \(c\).

When traveling upstream against the current, the steamer's speed is \(s - c\), and in 4.5 hours it covers a distance of \(4.5(s - c)\).

When traveling downstream with the current, the steamer's speed is \(s + c\), and in 3 hours it covers a distance of \(3(s + c)\).

Since both distances represent the distance between Towns A and B, we can equate them: \(4.5(s - c)=3(s + c)\), which gives \(s = 5c\). To express the distance in terms of only one unknown, substitute \(s = 5c\) in either of the above equations, to get \(3(s + c)=18c\).

To determine how long a raft, floating downstream at the speed of the current, will take to travel from Town B to Town A, we divide the distance between the towns by the speed of the raft: \(\frac{distance}{rate}=\frac{18c}{c}=18\) hours.


Answer: D