Esther drove to work at 45 miles per hour. Returned home at 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Ester drive to work in the morning?

Let the distance to work be x miles

time to : x/45
time fro : x/30

x/45 + x/30 = 1

solve for x:
I suggest multiplying each term by 90, the LCD, to clear fractions.

mainly i really don't know so goog d luck

To solve this problem, we can use the concept of speed and time.

Let's assume that Esther drove a distance D to work in the morning.

We know that her speed while driving to work was 45 miles per hour. So the time taken to drive to work can be calculated as D/45, since time = distance/speed.

On her way back home, Esther drove at a speed of 30 miles per hour. So the time taken to drive back home can be calculated as D/30.

We also know that the total commuting time was one hour. So the sum of the time taken to drive to work and the time taken to drive back home is equal to one hour:

D/45 + D/30 = 1

To solve this equation, we can find a common denominator and then simplify:

(2D + 3D)/90 = 1

5D/90 = 1

Cross multiplying, we get:

5D = 90

Dividing both sides by 5, we find:

D = 18

Therefore, Esther drove a distance of 18 miles to work in the morning.