At first, an athlete jogs at 5 miles per hour and then jogs at 6 miles per hour, traveling at 7 miles in 1.2 hours. How long does the athlete jog at each speed?

Question

Hint: Let t represent the amount of time the athlete jogs at 5 mph. Then 1.2 - 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.

Answer 1

should be: t*5 + (1.2-t)*6 = 7

so t=0.2 for 5m/h, 1hr for 6m/h



Answer 2

t*5 + (1.2-t)*7 = 7.

t represents time jogging at 5 mph and 1.2-t represents time jogging at 7 mph.

Expand the equation:

5t +8.4 - 7t = 7

-2t +8.4 = 7

Add 2t to both sides and subtract 7 from both sides

8.4 - 7 = 2t

1.4 = 2t

t = 0.7 hr @ 5mph and 1.2-t = 0.5 hr @ 7mph

Check: 5(0.7) + (1.2-.7)*7 = 3.5+3.5 = 7