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.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10