SOLUTION: A motorboat takes 3 hrs to travel 144 km going upstream the return trip takes 2 hrs going downstream what is the rate of the boat in still water and

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Question 445757: A motorboat takes 3 hrs to travel 144 km going upstream the return trip takes 2 hrs going downstream what is the rate of the boat in still water and what is the rate of the current.
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let c = the rate of the current
Let b = the speed of the boat in still water
given:
+d=+144+km+
time going upstream: +t%5B1%5D+=+3 hrs
time going downstream: +t%5B2%5D+=+2+ hrs
The equation going upstream:
+d+=+%28+b+-+c+%29%2At%5B1%5D+
(1) +144+=+%28+b+-+c+%29%2A3+
The equation going downstream:
+d+=+%28+b+%2B+c+%29%2At%5B2%5D+
(2) +144+=+%28+b+%2B+c+%29%2A2+
----------------------
There are 2 equations and 2 unknowns, so
it should be solvable
(1) +144+=+%28+b+-+c+%29%2A3+
(1) +3b+-+3c+=+144+
and
(2) +144+=+%28+b+%2B+c+%29%2A2+
(2) +2b+%2B+2c+=+144+
Multiply both sides of (1) by 2
and both sides of (2) by 3 and
subtract (1) from (2)
(2) +6b+%2B+6c+=+432+
(1) +-6b+%2B+6c+=+-288+
+12c+=+144+
+c+=+12+ km/hr
and
(2) +2b+%2B+2c+=+144+
(2) +2b+%2B+2%2A12+=+144+
(2) +2b+=+144+-+24+
(2) +2b+=+120+
+b+=+60+ km/hr
12 km/hr is the rate of the current
60 km/hr is the speed of the boat in still water

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
144/3 = 48 km/hr
144/2 = 72 km/hr
The boat's speed is the average (48+72)/2 = 60 km/hr
The current is the difference 72 - 60 = 12 km/hr