w=width of river
s1=speed of first boat
s2=speed of second boat
t1=time until boats meet the first time
t2=time until boats meet the second time
I shall arbitrarily say that both boats are 700 yards from the shore of original of the first boat at time t1.
The following equations can be inferred from the information given:
(1) w=t1*(s1+s2)
(2) s1*t1=700
(3) w+300=s1*t2
(4) 2w-300=s2*t2
Adding equations (1) and (2) we get:
(5) 3w=t2*(s1+s2)
Substituting s1+s2=w/t1 from equation (1) we get:
3w=t2*r/t1
3w*t1=r*t2
(6) 3*t1=t2
Combining equations (3) and (6):
(7) w+300=3*s1*t1
Combining equations (2) and (7):
w+300=2100
w=1800
This problem was asked in the 'Ask Marilyn' column in the November 19, 2000, issue of Parade magazine.
Michael Shackleford, ASA - November 18, 2000MathProblems.info home