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

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) (Show Source): You can put this solution on YOUR website!

------------
Let = distance in miles traveled at 5 mi/hr
= distance in miles traveled at 6 mi/hr
Let = time in hrs spent traveling at 5 mi/hr
= time in hrs spent traveling at 6 mi/hr
-------------------------------------------
Equation for traveling at 5 mi/hr
(1)
Equation for traveling at 6 mi/hr
(2)
----------------------------
(2)
(2)
(2)
and
(1)
Plug this into (2)
(2)
(2)
and
(1)
(1)
and

At 5 mi/hr, athelete jogged for .6 hrs
At 6 mi/hr athelete jogged for 1 hr
-------------------
check:
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK
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