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Answer:
the rate / speed of the boat is 10 miles per hour.
the rate / speed of the current is 2 miles per hour.
Step-by-step explanation:
r = rate of boat (speed of boat)
t = time
d = distance.
c = rate of current (speed of current)
with the current, the formula becomes (r + c) * t = d
against the current, the formula becomes (r - c) * t = d
going with the current, the boat takes 1 hour to travel 12 miles.
therefore:
(r + c) * t = d becomes (r + c) * 1 = 12
going against the current, the boat takes 1.5 hour to travel the same 12 miles.
therefore:
(r - c) * t = d becomes (r - c) * 1.5 = 12.
your two equations that need to be solved simultancously are:
(r + c) * 1 = 12
(r - c) * 1.5 = 12
divide both sides of the second equation by 1.5 and leave the first equaion as is to get:
r + c = 12
r - c = 8
add the equations together to get:
2 * r = 20
solve for r to get:
r = 20 / 2 = 10
(r + c) * 1 = 12 becomes (10 + c) * 1 = 12
simplify to get 10 + c = 12
solve for c to get c = 12 - 10 = 2
(r - c) * 1 = 8 becomes (10 - c) * 1 = 8
simplify to get 10 - c = 8
solve for c to get c = 10 - 8 = 2
you have:
r = 10
c = 2
that's your solution.
the rate / speed of the boat is 10 miles per hour.
the rate / speed of the current is 2 miles per hour.