1. ## Uhm what

Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?

2. Going to work;

Distance = Rate1 * Time1

Coming home from work;

Distance = Rate2 * Time2

_________________________

Rate1 = 45 Miles per hour (Mi/Hr)

Rate2 = 30 Miles per hour (Mi/Hr)

Time1 + Time2 = One Hour

" If Esther spent a total of one hour"

__________________________

Distance= 45Time1

Distance= 30Time2

Isolate time....

Therefore;

Distance/45 = Time1

Distance/30= Time2

Putting the equations together (Which is what the problem concerns)

Distance = 1/45 + 1/30

Make the denominators equivalent

1x2 = 2 , 45x2 = 90
1x3 = 3, 30x3 = 90

Distance = 2/90 + 3/90

Distance = 5/90

Simplify, Distance = 18

If you want to wait for someone else or look it up that's probably a better idea.

3. Originally Posted by Evelyn

Going to work;

Distance = Rate1 * Time1

Coming home from work;

Distance = Rate2 * Time2

_________________________

Rate1 = 45 Miles per hour (Mi/Hr)

Rate2 = 30 Miles per hour (Mi/Hr)

Time1 + Time2 = One Hour

" If Esther spent a total of one hour"

__________________________

Distance= 45Time1

Distance= 30Time2

Isolate time....

Therefore;

Distance/45 = Time1

Distance/30= Time2

Putting the equations together (Which is what the problem concerns)

Distance = 1/45 + 1/30

Make the denominators equivalent

1x2 = 2 , 45x2 = 90
1x3 = 3, 30x3 = 90

Distance = 2/90 + 3/90

Distance = 5/90

Simplify, Distance = 18