Christy drove 300 miles on her vacation. She drove 1.25 time faster on the second 150 miles of her trip than on the first. Which expression represents the time she spent driving? Let x be her speed for the fist half.
A. 375/x**
B.337.5/x
C.270x
D.270/x
Simplify x/6x-x^2
A. 1/6-x where x does not = 0x6
B. 1/6-x where x does not = 6
C. 1/6x where x does not = 0
D. 1/6**
Simplify 5x^3/7x^3+x^4
5/7+x; where x is not equal to 0, -7**
5/7+x; where x is not equal to -7
5/7x; where x is not equal to 0
5/7
#1
speed on first leg ---- x mph
speed on 2nd leg --- 1.25x mph
150/x + 150/1.25x
= 150/x + 120/x
= 270/x
#2, you must have meant:
x/(6x-x^2)
= x/(x(6 - x))
= 1/(6-x), x ≠ 0,6
#3 again watch you brackets
5x^3/7x^3+x^4
= 5x^3/(x^3(7 + x)
= 5/(7+x) , x ≠ 0,-7
To find the expression that represents the time Christy spent driving, let's break down the problem.
First, we know that Christy drove 300 miles in total. Let's assume her speed for the first 150 miles is x.
So, the time taken to drive the first 150 miles is 150/x.
Now, we are given that she drove 1.25 times faster on the second 150 miles of her trip than on the first. This means her speed for the second 150 miles would be 1.25x.
So, the time taken to drive the second 150 miles is 150/(1.25x).
The total time taken to drive 300 miles would be the sum of the time taken for the first and second halves:
Total time = 150/x + 150/(1.25x)
To simplify this expression, we can find a common denominator:
Total time = (150 * 1.25 + 150) / (1.25x)
Total time = (187.5 + 150) / (1.25x)
Total time = 337.5 / (1.25x)
Simplifying further, we get:
Total time = 270 / x
Therefore, the expression that represents the time Christy spent driving is 270/x.
The correct answer is (D) 270/x.
Now, let's simplify the expression x/6x - x^2.
To simplify, we can factor out an x from the numerator:
x/6x - x^2 = x(1/6 - x)
Therefore, the simplified expression is (A) 1/6 - x where x does not equal 0 or 6.
Finally, let's simplify the expression 5x^3 / (7x^3 + x^4).
We can see that both terms in the denominator can be factored out an x^3:
5x^3 / (7x^3 + x^4) = 5x^3 / (x^3(7 + x))
Now, we can cancel out the x^3 terms in the numerator and denominator:
5x^3 / (x^3(7 + x)) = 5 / (7 + x)
Therefore, the simplified expression is (B) 5 / (7 + x) where x does not equal 0 or -7.
To find the expression that represents the time Christy spent driving, we need to determine her speed for the first half and second half of the trip. Let's call her speed for the first half x.
If she drove 1.25 times faster on the second 150 miles, her speed for the second half would be 1.25x.
To determine the time spent driving, we divide the distance by the speed.
For the first half (150 miles), the time spent driving would be 150/x.
For the second half (150 miles), the time spent driving would be 150/(1.25x).
Adding the times for both halves, we get the total time spent driving: 150/x + 150/(1.25x).
Simplifying this expression further, we can divide both terms by 150 to get:
1/x + 1/(1.25x).
To find a common denominator, we multiply the first term by 1.25/1.25:
1.25/x + 1/(1.25x).
Combining the terms, we get:
(1.25 + 1)/(1.25x) = 2.25/(1.25x).
Therefore, the expression that represents the time Christy spent driving is 2.25/(1.25x).
Looking at the answer choices, the correct option is A. 375/x.