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?

The key is Esther travelled the same distance - x - in both her morning and evening commute.

45(time she took in the morning, or p) = x
30(time she took in the evening, or q) = x

Therefore 45(p) = 30(q), or divide both sides by 5 and get 9(p) = 6(q). I know you can divide it further, but these numbers are small enough and it's not worth the time.

Since the whole trip took an hour, (p + q) = 60min, and so, p = 60-q.

Therefore 9(60-q) = 6q or 540-9q = 6q. So 540 = 15q, which makes q = 36. If q = 36, then by (p+q)=60, p (the time she took in the morning) must equal 24.

45 miles per hour, her speed in the morning, times (24/60) hours, her time, makes 18 miles travelled in the morning. If you check, 30 miles per hour times (36/60) hours also makes 18 miles in the evening.

Hope that makes a little sense. And I also hope it's right

Let distance to work be x miles.
speed = 45 mph
so time = x/45 hours
return speed = 30 mph
return time = x/30

x/45+x/30 = 1
30x+45x / 30*45 =1
75x= 30*45
/75
x= 30*45/75

x=18 miles ... distance to work place

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

when multiplying or dividing by a negative on both sides you have to flip the inequality sign. this rule only applies to multiplying or dividing by a negative number in inequality equations. this rule is really important.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice

The answer is something i don’t know