Question 910315
rate(r) * time(t) = distance(d)
let r be the speed of the current and t1 + t2 = 10 and d = 200, then
let t1 be time with current and t2 time against current, then we have
t1 + t2 = 10
time with current is
t1 = 200 / (60+r)
time against current is
t2 = 200 / (60-r)
now we can add the two times
200/(60+r) + 200/(60-r) = 10
our lowest common denominator is (60+r)*(60-r)
200*(60-r) + 200*(60+r) = 10 * (60+r) * (60-r)
we can divide both sides of = by 10
20*(60-r) + 20*(60+r) = 3600 - r^2
simplify and combine like terms
1200 -20r + 1200 +20r = 3600 - r^2
2400 = 3600 -r^2
r^2 = 1200
r = square root of (1200) = 34.6 mph
speed of current is 34.6 mph