It will take adam four hours to drive to disney park, and 2.5 times less time if driving 45 mph faster. what is the distance adam should cover to get to the park?

  120 miles

Step-by-step explanation:

We have to "interpret" the problem statement, because its literal meaning is that it takes Adam a negative amount of time to drive the distance when driving faster. 2.5 times 4 hours is 10 hours. 10 hours less than 4 hours is -6 hours, meaning that driving faster gets Adam to the park 6 hours before he started driving.

So, we assume the intent of the problem is that driving faster multiplies Adam's travel time by a factor of 1/2.5, 2/5 of what it was at the lower speed. Since travel time is inversely proportional to speed, Adam's speed is effectively multiplied by 2.5 by driving faster. We can use the relation ...

  speed = distance/time

to relate the speeds (in mph) and times (in hours) given in the problem. For some distance d, we have ...

  45 + d/4 = 2.5(d/4) . . . . . adding 45 mph to his speed multiplies it by 2.5

Multiplying by 4 gives ...

  180 + d = 2.5d

  180 = 1.5d . . . . . . . . subtract d

  180/1.5 = d = 120 . . . divide by 1.5

Adam covers a distance of 120 miles to get to the park.

what is the model?

step-by-step explanation: