Question

12. Dreams of driving. Suppose you drive to school. If you

Answer 1

Answer: 12 miles

Step-by-step explanation:

Ok, we know that:

Distance = Time*Speed.

or:

D = T*S

The distance between the house and the school is constant, and suppose that T is the exact time such that you arrive just in time, then:

" If you  drive at an average speed of 45 mph, you arrive 1 min early  for the first bell. "

We can write this as:

D = (T - 1min)*45mi/h.

"If you drive at an average speed 40 mph,  you arrive 1 min late."

We can write this as:

D = (T + 1min)*40mi/h.

So we have a system of linear equations:

D = (T - 1min)*45mi/h.

D = (T + 1min)*40mi/h.

First, 1 hour has 60 mins, then 1 min = (1/60) hours.

We do this change because in the system of equations we have minutes and hours, and we can only work with one unit, now we can write the equations as:

D = (T - (1/60)h)*45mi/h.

D = (T + (1/60)h)*40mi/h.

now, we can write:

D = (T - (1/60)h)*45mi/h. = (T + (1/60)h)*40mi/h.

Now we can solve this for T.

(T - (1/60)h). = (T + (1/60)h)*(40/45)

T = (T + (1/60)h)*(40/45) + (1/60)h

T - T*40/45 = (1/60)h*(1 + 40/45) = 0.031 h

T*(1 - 40/45) = 0.031 h

T = 0.031h/(1 - 40/45) = 0.283... hours

Now, to find the distance to the school we can replace this time in one of the equations:

D = (T + (1/60)h)*40mi/h. = (0.283...h + (1/60)h)*40mi/h = 12 miles.