SOLUTION: Mike's workout consists of jogging for 3 miles and then riding his bike for 5 miles at a speed of 4 miles per hour faster than he jogs. If his total workout time is 1 hour, find hi

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Question 1042731: Mike's workout consists of jogging for 3 miles and then riding his bike for 5 miles at a speed of 4 miles per hour faster than he jogs. If his total workout time is 1 hour, find his jogging speed and his biking speed.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = his jogging speed in mi/hr
+s+%2B+4+ = his biking speed in mi/hr
Let +t+ = his time spent jogging in hrs
+1+-+t+ = his time spent biking in hrs
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Mike's equation for jogging:
(1) +3+=+s%2At+
Mike's equation for biking:
(2) +5+=+%28+s%2B4+%29%2A%28+1+-+t+%29+
---------------------------
(1) +t+=+3%2Fs+
Substitute (1) into (2)
(2) +5+=+%28+s%2B4+%29%2A%28+1+-+3%2Fs+%29+
(2) +5+=+s+%2B+4+-+3+-+12%2Fs+
(2) +4+=+s+-+12%2Fs+
(2) +4s+=+s%5E2+-+12+
(2) +s%5E2+-+4s+-+12+=+0+
(2) +%28+s+-+6+%29%2A%28+s+%2B+2+%29+=+0+ ( by inspection )
+s+=+6+ ( speed has to be positive )
and
+s+%2B+4+=+10+
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Mike's jogging speed is 6 mi/hr
Mike's biking speed is 10 mi/hr
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check:
(1) +3+=+s%2At+
(1) +3+=+6%2At+
(1) +t+=+1%2F2+ hr
and
(2) +5+=+%28+s%2B4+%29%2A%28+1+-+t+%29+
(2) +5+=+%28+6%2B4+%29%2A%28+1+-+t+%29+
(2) +5+=+10%2A%28+1+-+t+%29+
(2) +5+=+10+-+10t+
(2) +10t+=+5+
(2) +t+=+1%2F2+ hr
OK