SOLUTION: Good day! I get confused with word problems like this, can you lease help me? A boat can travel 48 km downstream in the same time it can travel 32 km upstream. If the rate of t

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Question 683899: Good day! I get confused with word problems like this, can you lease help me?
A boat can travel 48 km downstream in the same time it can travel 32 km upstream. If the rate of the boat in still water is 20 km/hr, find the rate of the current.
Thank you so much!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Hi. This type of problem has basically the same
setup for solution.
First, go to things they're looking for, and give it a name.
Let +c+ = the rate of the current in km/hr
+20+%2B+c+ = rate of boat going downstream in km/hr
+20+-+c+ = rate of boat going upstream in km/hr
+t+ = time in hrs for both trips
----------------------------
Equation for going downstream:
(1) +48+=+%28+20+%2B+c+%29%2At+
Equation for going upstream:
(2) +32+=+%28+20+-+c+%29%2At+
-------------------
There are 2 equations and 2 unknowns, so it's solvable
(1) +t+=+48+%2F+%28+20+%2B+c+%29+
Substitute (1) into (2)
(2) +32+=+%28+20+-+c+%29%2A%28+48+%2F+%28+20+%2B+c+%29+%29+
(2) +32%2A%28+20+%2B+c+%29+=+48%2A%28+20+-+c+%29+
(2) +640+%2B+32c+=+960+-+48c+
(2) +80c+=+960+-+640+
(2) +80c+=+320+
(2) +c+=+4+
The rate of the current is 4 km/hr
check:
(1) +48+=+%28+20+%2B+4+%29%2At+
(1) +48+=+24t+
(1) +t+=+2+
and
(2) +32+=+%28+20+-+4+%29%2At+
(2) +32+=+16t+
(2) +t+=+2+
OK