At first an athlete jogs at 4 miles per hour and then jogs at 8 miles per hour, traveling 10 miles in 1.5 hours. how long does the athlete jog at each speed? (hint: let t represent the amount of time the athlete jogs at 4 mph. then 1.5 minus t represents the amount of time the athlete jogs at 8 mph.)

we know

distance =time *speed

from given question we have following equation

4*t+(1.5-t)*8=10

4*t+12-8t=10

12-4t=10

-4t=10-12

4*t=2

t=0.5 hour

hence at speed 4 miles per hour he crosses 4*0.5=2 miles

at speed 8 miles per hour he crosses 8*(1.5-0.5)=8 miles

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