Family drives 1080 miles to lodge. average speed on return decreased by 6 miles per hour and trip took 2.5 hours longer. determine average speed on way to lodge.

  54 mph

Step-by-step explanation:

Let s represent the average speed on the way to the lodge. The relation between time, speed, and distance is ...

  time = distance/speed

so, the travel time to the lodge is 1080/s. The travel time on the return is 1080/(s-6). The difference in times is then ...

  1080/(s-6) -1080/s = 2.5

  1080s -1080(s-6) = 2.5(s)(s -6) . . . . multiply by s(s-6)

Now, we have a quadratic that can be solved in any of the usual ways.

  2.5s² -15s -6480 = 0 . . . . . . . . . . . . subtract the left side

  s² -6s -2592 = 0 . . . . . . . . . . . . . . . . divide by 2.5

  (s² -6s +9) -(2592 +9) = 0 . . . . . . . . complete the square

  (s -3)² = 51² . . . . . . . . . . . . . add 2601, write as squares

  s = 3 + 51 = 54 . . . . . . . . . . positive square root, add 3

The average speed on the way to the lodge was 54 mph.

b

step-by-step explanation: