SOLUTION: A boat traveled 25km upstream. On the return trip downstream, the boat traveled 5km per hour faster. It the trip took 10 minutes less time, what was the speed of the boat as it tra

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Question 18535: A boat traveled 25km upstream. On the return trip downstream, the boat traveled 5km per hour faster. It the trip took 10 minutes less time, what was the speed of the boat as it traveled upstream?
The answer is 25 km/hr but I don't know how to get to it!
Thanks for any help you can give!
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
Let the speed of the boat be x kmph
Distance upstream=25 km
Time=distance/speed=(25/x)hours


Now when going downstream,
distance=25 km
Speed of boat=(x+5)kmph [Given in question]
time taken=distance/speed=25/(x+5) hours


Now the time taken downstream was 10 minutes less than time taken upstream
10 minutes means (10/60)hours=(1/6)hours
This means that time taken taken to go downstream was less


So we get,
(time upstream)-(time downstream)=10 minutes
+%2825%2Fx%29-%2825%2F%28x%2B5%29%29=%281%2F6%29+
Taking LCM,
+%2825%28x%2B5%29-25%28x%29%29%2F%28x%28x%2B5%29%29=1%2F6+
+%2825x%2B25%285%29-25x%29%2F%28x%28x%2B5%29%29=1%2F6+
+%2825%285%29%29%2F%28x%28x%2B5%29%29=1%2F6+
Taking x(x+5) to the other side,
+25%285%29+=+%28x%28x%2B5%29%29%2F6+
+25%285%29%286%29+=+x%28x%2B5%29+
+25%2830%29+=+x%28x%2B5%29+
Taking everything to the right hand side we get,
+0+=+x%5E2+%2B+5x+-+25%2830%29+
Factoring this quadratic we get,
+x%5E2+-+25x+%2B+30x+-25%2830%29+=+0+
+%28x-25%29%28x%2B30%29+=+0+
x=25,-30
Speed cannot be negative
Therefore,x=25 kmph


So speed of the boat upstream was 25kmph


Hope this helps,
Prabhat