Problem: A particle moves so that its speed for the second and subsequent miles - varies inversely as the integral number of miles already traveled. For each subsequent mile the speed is constant. If the second mile is traversed in 2 hours, then the time, in hours, needed to traverse the nth mile is:
Answer Choices:
A. n−12
B. 2n−1
C. n2
D. 2 n
E. 2(n−1)
Solution:
Let vn be the speed for the n-th mile. Then vn=n−1k,n≧2.∴v2=2−1k=k. Since T=RD,2=v21=k1 so that k=21. Therefore, vn=2(n−1)1.∴Tn=vn1=2(n−1).