1. The time in hours, t=200/s, where s=speed. t-1=200/(s+10). So (t-1)(s+10)=200 and ts+10t-s-10=200. Therefore 10t-s=10 because st=200 causes 200 to cancel out. 10*200/s-s=10 and 2000-s^2=10s; s^2+10s-2000=0. This can be factorised: (s+50)(s-40)=0, so s=40 mph, since negative speeds can be ruled out.
2. Let s=speed of the boat. The actual speed of the boat when travelling against the current is s-3 and with the current is s+3. The distance is 60 miles. The total time is 60/(s-3)+60/(s+3)=9. Multiply through by s^2-9: 60(s+3+s-3)=9s^2-81. 120s=9s^2-81, 3s^2-40s-27=0. Using the quadratic formula: s=(40+sqrt(1600+4*3*27))/6=(40+sqrt(1600+324))/6=(20+sqrt(481))/3, giving s=13.98 mph, because the negative answer is rejected.
3. If the number of rows and columns is n, then n^2=c-24, where c=number of characters. (n+1)^2=c+25, because there is a surplus of 24 characters when they are arranged in n twos and columns, and a deficiency of 25 when they are arranged in n+1 rows and columns. (n+1)^2-n^2=2n+1=c+25-(c-24)=49, so 2n=48 and n=24. c-24=n^2=576, so c=600. The number of characters is therefore 600.