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Verdich [7]
3 years ago
11

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 ro

ute 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?
Mathematics
2 answers:
nydimaria [60]3 years ago
7 0
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.

<span>Hope that makes a little sense. And I also hope it's right</span>
professor190 [17]3 years ago
6 0
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






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Step-by-step explanation:

We know that she spent $16 dollars on magazines, so we can put it in the equation (16 + x= ?). We also know that the total is $112, so we can also add that (16+ x= 112). We don't know how many books she got, but we do know how much they cost (16 + 12x=112. So that makes  the books the variable (X).

To find the variable we need to take out the magazines from the price. 112-16=96. Now we're left with 12x=96. Now all we have to do is divide 96 by 12, which equals 8.

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3 years ago
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Masteriza [31]
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3 years ago
When placed in the box below, what expression will complete an example of the commutative property of addition 7(2+9)= ?
ANEK [815]

The expression for 7(2+9) IS A(B+C) which is distributive property of addition over multiplication.

Only two arithmetic procedures are subject to the commutative property: Multiplication and Addition

 A + B = B + A Which is Commutative property of addition

A.B = B.A, which is a commutative property of multiplication.

Distributive property is A(B+C) =AB+AC

The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical properties that is used the most. Commutative and associative qualities are the other two important features.

from the given data 7(2+9) =7*2+7*9

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Now, we can clear that 7(2+9) =7(9+2)

Hence, the expression for commutative property of addition is A(B+C) = AB+AC.

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1 year ago
PLEASE HELP!
Juliette [100K]

Answer: 135 miles

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3 years ago
Read 2 more answers
A system of linear equations has been graphed in the diagram. determine a reasonable solution for the system of equations.
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Answer:

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That is also known as the intersecting points.

The top-right part is known as the 1st Quadrant in a coordinate system.

Top-left is 2nd Quadrant.

Bottom left is 3rd Quadrant.

Bottom right is 4th Quadrant.

The values of x and y (positive or negative) of each quadrant is shown below:

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The intersection point (solution) of the 2 lines shown is in the 4th quadrant, which has x values positive and y values negative.

From the answer choices, we see that 3rd answer choice goes with this -- (1,-1), so this is the correct choice.

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