SOLUTION: Tina is training for a biathlon. To train for the running portion of the race, she runs 7 miles each day over the same course. The first 4 miles of the course is on level ground, w

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Question 1055874: Tina is training for a biathlon. To train for the running portion of the race, she runs 7 miles each day over the same course. The first 4 miles of the course is on level ground, while the last 3 miles is downhill. She runs 3 miles per hour slower on level ground than she runs downhill. If the complete course takes 1 hour, how fast does she run on the downhill part of the course?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs to run on the downhill part
+1+-+t+ = time in hrs to run on level ground
+s+ = speed in mi/hr running downhill
+s+-+3+ = speed in mi/hr running on level ground
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Equation for funning on level ground:
(1) +4+=+%28+s+-+3+%29%2A%28+1+-+t+%29+
Equation for running downhill:
(2) +3+=+s%2At+
-----------------------------
(2) +t+=+3%2Fs+
Plug (2) into (1)
(1) +4+=+%28+s+-+3+%29%2A%28+1+-+3%2Fs+%29+
(1) +4+=+s+-+3+-+3+%2B+9%2Fs+
(1) +10+=+s+%2B+9%2Fs+
Multiply both sides by +s+
(1) +10s+=+s%5E2+%2B+9+
(1) +s%5E2+-+10s+%2B+9+=+0+
(1) +%28+s+-+9+%29%2A%28+s+-+1+%29+=+0+ ( by looking at it )
I have to choose between
+s+=+9+ and
+s+=+1+
it can't be +s+=+1+ since
+s+-+3+ = speed in mi/hr running on level ground
and I would end up with negative speed
So, +s+=+9+
-------------------------------------
She runs 9 mi/hr on the downhill part
-------------------------------------
check:
(2) +t+=+3%2Fs+
(2) +t+=+3%2F9+
(2) +t+=+1%2F3+
and
(1) +4+=+%28+s+-+3+%29%2A%28+1+-+t+%29+
(1) +4+=+%28+9+-+3+%29%2A%28+1+-+t+%29+
(1) +4+=+6%2A%28+1+-+t+%29+
(1) +4+=+6+-+6t+
(1) +6t+=+6+-+4+
(1) +6t+=+2+
(1) +t+=+1%2F3+
OK