SOLUTION: A motorboat travels 448km in 8 hours going upstream and 258km in 3 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?

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Question 124110: A motorboat travels 448km in 8 hours going upstream and 258km in 3 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?
Answer by ankor@dixie-net.com(22740) (Show Source):
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A motorboat travels 448 km in 8 hours going upstream and 258 km in 3 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?
:
Let x = speed of boat in still water
Let y = speed of the current
then
(x-y) = Upstream speed
(x+y) = downstream speed
:
Write a distance equation for each trip; (Distance = time * speed)
:
Upstream trip equation:
8(x - y) = 448
Simplify, divide both sides by 8; resulting in:
x - y = 56
:
Downstream trip equation:
3(x + y) = 258
Simplify, divide both sides by 3: resulting in:
x + y = 86
:
Use these two equations for elimination:
x - y = 56
x + y = 86
--------------adding eliminates y, find x.
2x = 142
x =
x = 71 km/hr in still water
:
Find y using x + y = 86 to find y, substitute 71 for x:
71 + y = 86
y = 86 - 71
y = 15 km/hr is the current;
:
Check our solution in the upstream trip equation
8(71 - 15) =
8 * 56 = 448 km