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Question

Esther drove to work at an average speed of 45 miles/hr. She drove back home at an average speed of 30 miles/hr. The total time she drove was one hour. How many miles did Esther drive in the morning?

Answer 1

Let

x/45 = rate ester drove to word

x/30 = rate ester drove bach home

1= total time

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x/45 + x/30 = 1

90(x/45) + 90(x/30) = 90(1)

2x + 3x = 90

5x = 90

5x/5 = 90/5

x = 90/5

x = 18

The distance travele is 18 miles

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Answer 2

Let x be the distance from home to office. In the morning she took x/45 hours and in the evening, she took x/30 hours. The total is 1 hour. So let us write the equation:

x/45 + x/30 = 1

The common denominator is 90.

That gives 2x + 3x = 90
5x = 90 or x = 18 miles.

Let us check.

She takes 18X60/45 minutes in the morning and 18X60/30 minutes in the evening. Adding them, we have 24 + 36 minutes which add up to 60 minutes or 1 hour.

Answer 3

Let d be the distance travelled in the morning. Then

d/45 + d/30 = 1.

Mutiplying through by 90 yields

2d + 3d = 5d = 90

and dividing through by 90 yields

d = 18.

Hence the distance travelled was 18 miles.