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.
