SOLUTION: a motorboat can maintain a constant speed of 23 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 29 minutes.the return trip takes 17 minut

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Question 971136: a motorboat can maintain a constant speed of 23 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 29 minutes.the return trip takes 17 minutes. What is the speed of the current?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
a motorboat can maintain a constant speed of 23 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 29 minutes.the return trip takes 17 minutes. What is the speed of the current?
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Upstream DATA:
time = 29/60 hr ; distance = x miles ; rate = x/(29/60) = 60x/29 mph
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Downtream Data::
time = 17/60 hr ; distance = x miles ; rate = 60x/17 mph
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Equations to find speed of current:
Up stream:: 60x/29 = 23-c
Downstream: 60x/17 = 23+c
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Add and solve for "x"
60x/29 + 60x/17 = 46
17*60x + 29*60x = 17*29*46
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46*60x = 17*29*46
60x = 17*29
x = 8.22 miles
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Xolve for "c"::
c = 60x/17 - 23
c = 6 mph (speed of the current)
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = the speed of the current in mi/hr
= the boat's speed going upstream in mi/hr
= the boat's speed going downstream in mi/hr
Let = the one-way distance in mi
--------------------------------
Going upstream:
(1)
( note that I converted minutes to hours )
--------------------------------------
Going downstream:
(2)
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Substitute (2) into (1)
(1)
Multiply both sides by
(1)
(1)
(1)
(1)
(1)
The speed of the current is 6 mi/hr
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check:
(1)
(1)
(1)
(1)
(1) mi
-----------------------
(2)
(2)
(2)
(2) mi
OK