SOLUTION: It takes a couple four hours to row 28 miles with the river current. If it takes them 7 hours to cover the same distance when rowing against the current, find the speed of the rive

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Question 270049: It takes a couple four hours to row 28 miles with the river current. If it takes them 7 hours to cover the same distance when rowing against the current, find the speed of the river current
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
b = speed of boat in still water
c = speed of current
With the current:
d+=+%28b+%2B+c%29%2At%5B1%5D
Against the current:
d+=+%28b+-+c%29%2At%5B2%5D
----------------------
given:
d+=+28 mi
t%5B1%5D+=+4 hrs
t%5B2%5D+=+7 hrs
-----------------------
d+=+%28b+%2B+c%29%2At%5B1%5D
28+=+%28b+%2B+c%29%2A4
(1) 4b+%2B+4c+=+28
and
d+=+%28b+-+c%29%2At%5B2%5D
28+=+%28b+-+c%29%2A7
(2) 7b+-+7c+=+28
----------------------
(1) 4b+%2B+4c+=+28
(1) b+%2B+c+=+7
and
(2) 7b+-+7c+=+28
(2) b+-+c+=+4
and
(2) b+%2B+c+=+7
(1) b+-+c+=+4
2b+=+11
b+=+5.5
And, from (2),
b+-+c+=+4
5.5+-+c+=+4
c+=+5.5+-+4
c+=+1.5
The speed of the river current is 1.5 mi/hr
check:
28+=+%28b+%2B+c%29%2A4
28+=+%285.5+%2B+1.5%29%2A4
28+=+7%2A4
28+=+28
and
28+=+%28b+-+c%29%2A7
28+=+%285.5+-+1.5%29%2A7
28+=+4%2A7
28+=+28
OK