Problem: A privateer discovers a merchantman miles to leeward at a.m. and there being a good breeze bears down upon her at mph while the merchantman can only make mph in her attempt to escape. After a two hour chase, the top sail of the privateer being carried away, she can make only miles while the merchantman makes . The privateer will overtake the merchantman at:
Answer Choices:
A. p.m.
B. p.m.
C. p.m.
D. p.m.
E. p.m.
Solution:
After the two-hour chase, at P.M. the distance between the two ships is miles. Let be the number of hours needed for the privateer to overtake the merchantman. Let and be the distances covered in hours by the merchantman and the privateer, respectively. Then Rate of merchantman , and Rate of privateer or
hours, so that the ships meet at .