SOLUTION: Latoya swam 5 kilometers against the current in the same amount of time it took her to swim 15 kilometers with the current. The rate of the current was 2 kilometers per hour. How

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Question 1039013: Latoya swam 5 kilometers against the current in the same amount of time it took her to swim 15 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Latoya swim if there were no current?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her speed in the water with no current
in km/hr
Let +t+ = her time in hrs for swimming either
5 km or 15 km
---------------------------
Equation for swimming against the current:
(1) +5+=+%28+s+-+2+%29%2At+
Equation for swimming with the current:
(2) +15+=+%28+s+%2B+2+%29%2At+
-----------------------
(1) +t+=+5+%2F+%28+s+-+2+%29+
Substitute (1) into (2)
(2) +15+=+%28+s+%2B+2+%29%2A%28+5+%2F+%28+s+-+2+%29+%29+
Multiply both sides by +s+-+2+
(2) +15%2A%28+s+-+2+%29+=+5%2A%28+s+%2B+2+%29+
(2) +15s+-+30+=+5s+%2B+10+
(2) +10s+=+40+
(2) +s+=+4+
----------------
Her speed swimming with no current is 4 km/hr
----------------
check answer:
(1) +5+=+%28+s+-+2+%29%2At+
(1) +5+=+%28+4+-+2+%29%2At+
(1) +5+=+2t+
(1) +t+=+5%2F2+
and
(2) +15+=+%28+s+%2B+2+%29%2At+
(2) +15+=+%28+4+%2B+2+%29%2At+
(2) +15+=+6t+
(2) +t+=+15%2F6+
(2) +t+=+5%2F2+
OK