Question
The current of a river moves at 3 miles per hour. It takes a boat 3 hours to travel 12 miles upstream, against the current, and return the same distance traveling downstream, with the current. What is the boats rate in still water?
Answers
boat's speed in still water --- x mph
against the current ----- x-3 mph
with the current -------- x + 3 mph
time against current = 12/(x-3)
time with the current = 12/(x+3)
12/(x+3) + 12/(x-3) = 3
times (x-3)(x+3) or x^2 - 9
12(x-3) + 12(x+3) = 3(x^2 - 9)
12x-36 + 12x + 36 = 3x^2 - 27
3x^2 - 24x - 27 = 0
x^2 - 8x - 9 = 0
(x-9)(x+1) = 0
x = 9 or x = -1, I guess we'll reject that negative
the boat's speed in calm water is 9 mph
check:
12/12 + 12/6
= 1 + 2
= 3hrs.
against the current ----- x-3 mph
with the current -------- x + 3 mph
time against current = 12/(x-3)
time with the current = 12/(x+3)
12/(x+3) + 12/(x-3) = 3
times (x-3)(x+3) or x^2 - 9
12(x-3) + 12(x+3) = 3(x^2 - 9)
12x-36 + 12x + 36 = 3x^2 - 27
3x^2 - 24x - 27 = 0
x^2 - 8x - 9 = 0
(x-9)(x+1) = 0
x = 9 or x = -1, I guess we'll reject that negative
the boat's speed in calm water is 9 mph
check:
12/12 + 12/6
= 1 + 2
= 3hrs.