Answer to Question #175307 in Algebra for Dawson

Question

At first an athlete jogs at 6 miles per hour and then jogs at 8 miles per​ hour, traveling 11 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 6 mph. Then 1.5 − t represents the amount of time the athlete jogs at 8 mph.)

The athlete jogged blank hour (s) at a speed of 6 miles per hour and blank hour (s) at a speed of 8 miles per hour.

Answer 1

Total Distance Covered = 11 miles

Total Time = 1.5 Hours

Let the athlete jogs t hours at a speed of 6 mph and covers x miles.

Therefore,

Speed = Distance / Time

6 = x/t

Or, x = 6t --- Eqn. 1

And, therefore, the balance distance = 11 - x

And Balance Time = 1.5 - t

Given Speed = 8 mph

Therefore,

Speed = Distance / Time

8 = (11 - x) / (1.5 - t)

On solving above, we get,

12 - 8t = 11 - x

Or

8t - x = 1 --- Eqn. 2

Put x = 6t from Eqn. 1 in Eqn. 2, we get,

8t - 6t = 1

Or

t = 1/2 hours =0.5 Hours (30 minutes) (at a speed of 6 mph)

Therefore, Balance Time = 1.5 - 0.5 = 1 Hour (at a speed of 8mph)

Final Answer:

The athlete jogs for half an hour at a speed of 6mph (covering 3 miles) and 1 hour at a speed of 8mph (covering 8 miles).