SOLUTION: James takes 1(1/2) times as long to go 48 miles upstream as he does to return. If the boat cruises at 20 mph in still water, what is the speed of the current?

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Question 1021345: James takes 1(1/2) times as long to go 48 miles upstream as he does to return. If the boat cruises at 20 mph in still water, what is the speed of the current?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = his time in hrs to go downstream
+%283%2F2%29%2At+ = his time in hrs to go upstream
Let +c+ = the speed of the current
------------------------------
His equation for going downstream:
(1) +48+=+%28+20+%2B+c+%29%2At+
His equation for going upstream:
(2) +48+=+%28+20+-+c+%29%2A%28+%283%2F2%29%2At+%29+
--------------------------------
(1) +t+=+48%2F%28+20+%2B+c+%29+
Plug (1) into (2)
(2) +48+=+%28+20+-+c+%29%2A+%283%2F2%29%2A%28+48+%2F+%28+20+%2B+c+%29+%29+
Multiply both sides by +2%2A%28+20+%2B+c+%29+
(2) +2%2A48%2A%28+20+%2B+c+%29+=+%28+20+-+c+%29%2A3%2A48+
Divide both sides by +48+
+2%2A%28+20+%2B+c+%29+=+3%2A%28+20+-+c+%29+
+40+%2B+2c+=+60+-+3c+
+5c+=+20+
+c+=+4+
the speed of the current is 4 mi/hr
-----------------------------
check:
(1) +48+=+%28+20+%2B+c+%29%2At+
(1) +48+=+%28+20+%2B+4+%29%2At+
(1) +48+=+24t+
(1) +t+=+2+
and
(2) +48+=+%28+20+-+c+%29%2A%28+%283%2F2%29%2At+%29+
(2) +48+=+%28+20+-+4+%29%2A%28+%283%2F2%29%2At+%29+
(2) +48+=+16%2A%283%2F2%29%2At+
(2) +48+=+24t+
(2) +t+=+2+
OK