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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = boat's maximum speed in still water in mi/hr
+s+%2B+2+ = boat's maximum speed going downstream in mi/hr
+s+-+2+ = boat's maximum speed going upstream in mi/hr
Let +t+ = boat's time in hrs to go 8 mi downstream
+2+-+t+ = boat's time in hrs to go 4 mi upstream
---------------------
Going downstream:
(1) +8+=+%28+s+%2B+2+%29%2At+
Going upstream:
(2) +4+=+%28+s+-+2+%29%2A%28+2+-+t+%29+
--------------------------
(1) +t+=+8%2F%28+s%2B2+%29+
and
(2) +4+=+%28+s+-+2+%29%2A%28+2+-+t+%29+
(2) +4%2F%28+s-2+%29+=+2+-+t+
(2) +4%2F%28+s-2+%29+=+2+-+8%2F%28+s%2B2+%29+
Multiply both sides by +%28+s-2+%29%2A%28+s%2B2+%29+
(2) +4%2A%28+s%2B2+%29+=+2%2A%28+s%2B2+%29%2A%28+s-2+%29+-+8%2A%28+s-2+%29+
(2) +4s+%2B+8+=+2%2A%28+s%5E2+-+4+%29+-+8s+%2B+16+
(2) +4s+%2B+8+=+2s%5E2+-+8+-+8s+%2B+16+
(2) +2s%5E2+-+12s+=+0+
(2) +s%2A%28+2s+-+12+%29+=+0+
The solutions are:
+s+=+0+ ( the boat is drifting with the current )
+s+=+6+
----------------
the boat's maximum speed in still water is 6 mi/hr
----------------
check:
(1) +8+=+%28+s+%2B+2+%29%2At+
(1) +8+=+%28+6+%2B+2+%29%2At+
(1) +8+=+8t+
(1) +t+=+1+ hr
and
(2) +4+=+%28+s+-+2+%29%2A%28+2+-+t+%29+
(2) +4+=+%28+6+-+2+%29%2A%28+2+-+t+%29+
(2) +4+=+4%2A%28+2+-+t+%29+
(2) +4+=+8+-+4t+
(2) +4t+=+8+-+4+
(2) +4t+=+4+
(2) +t+=+1+ hr
+t+%2B+%28+2-t+%29+=+2+
+1+%2B+1+=+2+
OK


Answer by MathTherapy(10552) About Me  (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%2F%28S+%2B+2%29+%2B+4%2F%28S+-+2%29+=+2

8(S - 2) + 4(S + 2) = 2(S + 2)(S - 2) -------- Multiplying by LCD, (S + 2)(S - 2)

8S+%2B+16+%2B+4S+%2B+8+=+2%28S%5E2+-+4%29

12S+%2B+24+=+2S%5E2+-+8

2S%5E2+-+12S+-+24+-+8+=+0

2S%5E2+-+12S+-+32+=+0

2%28S%5E2+-+6S+-+16%29+=+2%280%29

S%5E2+-+6S+-+16+=+0

(S - 8)(S + 2) = 0

S, or speed in still water = highlight_green%286%29 mph    OR    S = - 2 (ignore)