When Amy drives her car to work, the trip takes 1/2 hour. When she rides the bus, it takes 3/4 hour. The average speed of the bus is 12 mph less than her speed driving. Find the distance she travels to work.

X mi/h = Molly's speed.

(X-12)mi/h = Bus's speed.
Mary's distance and the bus's are equal:
d1 = d2
0.5*x = 0.75(x-12)
Multiply both sides by 4:
2x = 3x - 36
2x - 3x = -36
-x = 36
X = 36 mi/h.
d = V*t = 36 * 0.5 = 18 Mi.

To find the distance Amy travels to work, we need to use the formula:

Distance = Speed × Time.

Let's start by assigning some variables:
Let D be the distance she travels to work in miles.
Let S be the speed at which Amy drives in mph.

We know that the trip by car takes 1/2 hour, so the time taken by car is 1/2 hour. Similarly, the trip by bus takes 3/4 hour, so the time taken by bus is 3/4 hour.

From the information given, we also know that the average speed of the bus is 12 mph less than Amy's speed driving. Therefore, the speed of the bus is S - 12 mph.

Now, let's calculate the distance traveled by Amy when driving and when taking the bus:

Distance by car = S × (1/2) = S/2 miles.
Distance by bus = (S - 12) × (3/4) = 3S/4 - 9 miles.

Since both distances are equal (Amy is traveling the same distance), we can set up an equation:
S/2 = 3S/4 - 9.

Now, let's solve the equation to find the value of S:

Multiply both sides of the equation by 4 to eliminate fractions:
4(S/2) = 4(3S/4 - 9).
2S = 3S - 36.

Subtract 3S from both sides of the equation:
2S - 3S = -36.
-S = -36.

Divide both sides of the equation by -1:
S = 36.

The speed at which Amy drives is 36 mph.

To find the distance she travels to work, substitute S = 36 into the formula Distance = Speed × Time:

Distance = 36 × (1/2) = 18 miles.

Therefore, Amy travels 18 miles to work.