Problem: At his usual rate a man rows 15 miles downstream in five hours less time than it takes him to return. If he doubles his usual rate, the time downstream is only one hour less than the time upstream. In miles per hour, the rate of the stream's current is:
Answer Choices:
A. 2
B. 25
C. 3
D. 27
E. 4
Solution:
Let m (miles per hour) be the man's rate in still water, and let c (miles per hour) be the rate of the current. Then
m+c15=m−c15−515m−15c=15m+15c−5m2+5c2∴−5m2+5c2=−30c∴m2−4c2=0,and2m+c15=2m−c15−1and30m−15c=30m+15c−4m2+c2and−4m2+c2=−30cm=2c,3c2=6c,c=2