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sammy [17]
3 years ago
8

Lizette is training for a marathon. At 7:00 she left her house and ran until 8:30, then she walked until 11:30. She covered a to

tal distance of 18 miles. Her running speed was six miles per hour faster than her walking speed. Find her running and walking speeds in miles per hour.
Mathematics
2 answers:
Leokris [45]3 years ago
6 0
<h3>Answer:</h3>
  • running speed: 8 mph
  • walking speed: 2 mph
<h3>Step-by-step explanation:</h3>

Let w represent Lizette's walking speed. Then her running speed is w+6. The relationship between speed, time, and distance is ...

  distance = speed × time

Lizette ran for 1.5 hours, then walked for 3 hours. Her total distance is ...

  (w+6)·1.5 + w·3 = 18

  4.5w + 9 = 18 . . . . . simplify

  4.5w = 9 . . . . . . . . . subtract 9

  w = 2 . . . . . . . . . . . .divide by 4.5

Lizette's walking speed is 2 mph; her running speed is 8 mph.

Cerrena [4.2K]3 years ago
6 0

Answer:

Walking speed = 2 mph.

Running speed = 8 mph.

Step-by-step explanation:

Let her walking speed be x mph, then her running speed is x + 6 mph

Speed = distance / time. Take the first 1 1/2 hours:

x + 6 =  y / 1.5   where y = distance travelled in that time

rewriting:

x + 6 = 2y / 3...........(1)

And the last 3 hours:

x = z / 3.......... (2)  where z = distance travelled in that time.

Also we have the equation:

y + z = 18..........(3)

Substitute x = z/3 into equation (i):

z/3 + 6 = 2y/3

Multiply through by 3:

z + 18 = 2y

2y - z = 18 ............(4)

y + z = 18..........(3)   Adding these 2 equations:

3y = 36

y = 12 miles,

So z = 18 - 12 = 6 miles.

Now find  the value of x:

From equation (2):

x =  z/ 3

= 6/3

= 2 mph.

Therefore running speed = 2 + 6 = 8 mph.

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Explain how you would convert a measurement given in ounces in pints
Tom [10]

Answer:

It is known that 1 pint equals 16 ounces

Step-by-step explanation:

It is known that 1 pint equals 16 ounces. Then we use this data to transform a number of ounces into pints.

Suppose we have x ounces. We want to know how many pints are these x ounces. Then we perform the following operation

x\ ounces*\frac{1\ pint}{16\ ounces}=z\ pints

Where z pints is the amount equivalent to x ounces

6 0
3 years ago
Please help :)))) ( attachment )
Anastaziya [24]
Let,
f(x) = -2x+34
g(x) = (-x/3) - 10
h(x) = -|3x|
k(x) = (x-2)^2

This is a trial and error type of problem (aka "guess and check"). There are 24 combinations to try out for each problem, so it might take a while. It turns out that 

g(h(k(f(15)))) = -6
f(k(g(h(8)))) = 2

So the order for part A should be: f, k, h, g
The order for part B should be: h, g, k f
note how I'm working from the right and moving left (working inside and moving out).


Here's proof of both claims

-----------------------------------------

Proof of Claim 1:

f(x) = -2x+34
f(15) = -2(15)+34
f(15) = 4
-----------------
k(x) = (x-2)^2
k(f(15)) = (f(15)-2)^2
k(f(15)) = (4-2)^2
k(f(15)) = 4
-----------------
h(x) = -|3x|
h(k(f(15))) = -|3*k(f(15))|
h(k(f(15))) = -|3*4|
h(k(f(15))) = -12
-----------------
g(x) = (-x/3) - 10
g(h(k(f(15))) ) = (-h(k(f(15))) /3) - 10
g(h(k(f(15))) ) = (-(-12) /3) - 10
g(h(k(f(15))) ) = -6

-----------------------------------------

Proof of Claim 2:

h(x) = -|3x|
h(8) = -|3*8|
h(8) = -24
---------------
g(x) = (-x/3) - 10
g(h(8)) = (-h(8)/3) - 10
g(h(8)) = (-(-24)/3) - 10
g(h(8)) = -2
---------------
k(x) = (x-2)^2
k(g(h(8))) = (g(h(8))-2)^2
k(g(h(8))) = (-2-2)^2
k(g(h(8))) = 16
---------------
f(x) = -2x+34
f(k(g(h(8))) ) = -2*(k(g(h(8))) )+34
f(k(g(h(8))) ) = -2*(16)+34
f(k(g(h(8))) ) = 2
5 0
3 years ago
In April, the number of cars sold was 546.
Maksim231197 [3]

Answer:

520 cars

Step-by-step explanation:

Let the car sold in March be x, x+5%*x=546. (105/100)*x=546. x=520

4 0
3 years ago
Pedro had $235 in his saving account when Jim had $450 in his account. Look at the situation in the image. Which inequality show
11111nata11111 [884]

Answer:

$450>$235

Step-by-step explanation:

This is because, when 235 is subtracted from 450 there is a great difference thats why $450 is greater than $235

4 0
2 years ago
The amount $180.00 is what percent greater than $135.00? A. 25% B. 33.33% C. 35% D. 133.33%
pav-90 [236]
180/135=133.33
Therefore the answer is B; 33.33%
Hope this helps!
6 0
3 years ago
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