SOLUTION: If you can run 10 kilometers per hour faster than your friend , and can keep that rate up until you reach your destination 60 kilometers away. If you and your friend start running

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Question 1003188: If you can run 10 kilometers per hour faster than your friend , and can keep that rate up until you reach your destination 60 kilometers away. If you and your friend start running at the same time and your friend arrives one hour after you , how fast did you run
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = your speed in km/hr
+s+-+10+ = your friend's speed in km/hr
Let +t+ = your time in hrs to reach destination
+t+%2B+1+ = your friend's time in hrs
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Your equation:
(1) +60+=+s%2At+
Your friend's equation:
(2) +60+=+%28+s-10+%29%2A%28+t%2B1+%29+
-------------------------
(1) +t+=+60%2Fs+
and
(2) +60+=+%28+s+-+10+%29%2A%28+60%2Fs+%2B+1+%29+
(2) +60+=+60+-+600%2Fs+%2B+s+-+10+
(2) +10+=+s+-+600%2Fs+
(2) +10s+=+s%5E2+-+600+
(2) +s%5E2+-+10s+-+600+=+0+
I can see by looking at it:
(2) +%28+s+-+30+%29%2A%28+s+%2B+20+%29+=+0+
Use the positive answer:
+s+=+30+
You ran 30 km/hr
----------------
check:
(1) +60+=+s%2At+
(1) +60+=+30%2At+
(1) +t+=+2+
and
(2) +60+=+%28+s-10+%29%2A%28+t%2B1+%29+
(2) +60+=+%28+30-10+%29%2A%28+t%2B1+%29+
(2) +60+=+20%2A%28+t%2B1+%29+
(2) +60+=+20t+%2B+20+
(2) +20t+=+40+
(2) +t+=+2+
OK