SOLUTION: at first an athlete jogs at 5 miles per hour and then jogs at 6 miles per hour, traveling 9 miles in 1.6 hours. How long does the athlete jog at each speed? (T represents the amou

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Question 1026312: at first an athlete jogs at 5 miles per hour and then jogs at 6 miles per hour, traveling 9 miles in 1.6 hours. How long does the athlete jog at each speed? (T represents the amount of time the athlete jogs at 5 mph. Then 1.6 -t represents the amount of time the athlete jogs at 6 mph)
The athlete jogged ( ) hour(s) at a speed of 5 miles per hour and ( )hour(s) at a speed of 6 miles per hour. (type integers or decimals)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+d+=+r%2At+
+t+=+d%2Fr+
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Let +d+ = distance in miles traveled at 5 mi/hr
+9+-+d+ = distance in miles traveled at 6 mi/hr
Let +t+ = time in hrs spent traveling at 5 mi/hr
+1.6+-+t+ = time in hrs spent traveling at 6 mi/hr
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Equation for traveling at 5 mi/hr
(1) +t+=+d%2F5+
Equation for traveling at 6 mi/hr
(2) +1.6+-+t+=+%28+9+-+d+%29+%2F+6+
----------------------------
(2) +6%2A%28+1.6+-+t+%29+=+9+-+d+
(2) +9.6+-+6t+=+9+-+d+
(2) +6t+-+d+=+.6+
and
(1) +d+=+5t+
Plug this into (2)
(2) +6t+-+5t+=+.6+
(2) +t+=+.6+
and
(1) +d+=+5%2A.6+
(1) +d+=+3+
and
+1.6+-+t+=+1.6+-+.6+
+1.6+-+t+=+1+
At 5 mi/hr, athelete jogged for .6 hrs
At 6 mi/hr athelete jogged for 1 hr
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check:
(1) +t+=+d%2F5+
(1) +.6+=+3%2F5+
(1) +3+=+3+
and
(2) +1.6+-+t+=+%28+9+-+d+%29+%2F+6+
(2) +1.6+-.6+=+%28+9+-+3+%29+%2F+6+
(2) +1+=+6%2F6+
(2) +1+=+1+
OK