SOLUTION: Traveling at full speed on a river, it takes 2 hours for a motorboat to travel 8 miles downstream and 4 miles back upstream. If the current's speed is 2mph, what is the maximum spe

Question 989697: Traveling at full speed on a river, it takes 2 hours for a motorboat to travel 8 miles downstream and 4 miles back upstream. If the current's speed is 2mph, what is the maximum speed of the boat in still water?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = boat's maximum speed in still water in mi/hr
= boat's maximum speed going downstream in mi/hr
= boat's maximum speed going upstream in mi/hr
Let = boat's time in hrs to go 8 mi downstream
= boat's time in hrs to go 4 mi upstream
---------------------
Going downstream:
(1)
Going upstream:
(2)
--------------------------
(1)
and
(2)
(2)
(2)
Multiply both sides by
(2)
(2)
(2)
(2)
(2)
The solutions are:
( the boat is drifting with the current )

----------------
the boat's maximum speed in still water is 6 mi/hr
----------------
check:
(1)
(1)
(1)
(1) hr
and
(2)
(2)
(2)
(2)
(2)
(2)
(2) hr

OK

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Traveling at full speed on a river, it takes 2 hours for a motorboat to travel 8 miles downstream and 4 miles back upstream. If the current's speed is 2mph, what is the maximum speed of the boat in still water?

Let speed of boat in still water be S
Total speed when travelling downstream: S + 2
Total speed when travelling upstream: S - 2
We can then form the following TIME equation:
8(S - 2) + 4(S + 2) = 2(S + 2)(S - 2) -------- Multiplying by LCD, (S + 2)(S - 2)

(S - 8)(S + 2) = 0
S, or speed in still water = mph OR S = - 2 (ignore)
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