SOLUTION: A boat travels 150 miles downstream with the current in 6 hours and 114 upstream against the current in the same amount of time.Find the speed of the current and the speed of the b

Question 515497: A boat travels 150 miles downstream with the current in 6 hours and 114 upstream against the current in the same amount of time.Find the speed of the current and the speed of the boat in still water. Please include variables and representation.
Found 2 solutions by oberobic, drcole:
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
150 miles in 6 hr = 150/6 = 25 mph
.
114 miles in 6 hr = 114/6 = 19 mph
.
s = boat speed in still water
c = current
r = rate
.
Going down stream
r = s+c = 25 mph
.
Going upstream
r = s-c = 19 mph
.
s + c = 25
s - c = 19
----------
2s = 44
s = 22
.
c = 25-22 = 3
.
The speed of the boat in still water is 22 mph.
The speed of the current is 3 mph.
.
Check the solution.
.
6 hr * 25 = 150 miles
6 hr * 19 = 114 miles
Correct.
.
Done.
Answer by drcole(72) (Show Source): You can put this solution on YOUR website!
Let s be the speed of the boat in still water, and let r be the speed of the current (both in mph). The speed of the boat downstream will be the sum of the speed of the boat in still water and the speed of the current, or s + r. We know that the boat traveled 150 miles downstream in 6 hours, so the speed of the boat downstream was
mph
So we have the algebraic equation:
s + r = 25
The speed of the boat upstream will be the speed of the boat in still water minus the speed of the current, or s - r. We know that the boat traveled 114 miles upstream in 6 hours, so the speed of the boat upstream was
mph
This gives us the algebraic equation:
s - r = 19
We now have a system of two linear equations in two unknowns. We can solve this system using elimination: if we add the second equation to the first equation, we cancel out r and are left with an equation involving s only:
s + r = 25
s - r = 19
----------
2s = 44 (summing the two equations, eliminating r)
s = 22
So the speed of the boat in still water was 22 mph. We now substitute 22 for s into the first equation and solve for s:
22 + r = 25 (substituting 22 for s in the first equation)
r = 3 (subtracting 22 from both sides)
So the speed of the current was 3 mph.
Let's check if this works. As the boat heads downstream, its speed will be 22 + 3 = 25 mph, so after 6 hours, it would travel 150 miles, which is what we wanted. As the boat heads upstream, its speed will be 22 - 3 = 19 mph, so after 6 hours, it would travel 114 miles, which is also what we wanted. So we have the correct answer.
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