Ask question

Ask question

All categories

3 years ago

10

It takes Max three hours to run 30 kilometers. Georges, on the other hand, travels the same distance in 2 hours and 20 minutes.

If both are to complete a 15-kilometre race, how long before Max will Georges arrive to the finish line?

1 answer:

Mamont248 [21]3 years ago

3 0

George will arrive 20 minutes before Max

It takes Max 3 hours(180 minutes) to run 30 km .

The rate can be calculated as follows:

rate = 30 / 180 = 1/6 km/ min

George uses 2 hours 20 minutes(140 minutes) to run 30 km.

The rate can be calculated as follows:

rate = 30 / 140 = 3/14 km / min

If both are to complete a 15-kilometre race, Therefore,

Max time will be

1 / 6 = 15 / t

t = 15 × 6

t = 90 minutes

George time will be

3/14 = 15 / t

3t = 210

t = 210 / 3

t = 70 minutes

Time difference = 90 - 70 = 20 minutes

Therefore, George will arrive 20 minutes earlier than Max

read more: brainly.com/question/18594378?referrer=searchResults

You might be interested in

What is 817x45 in standerd algorithm pls help

sineoko [7]

Answer:

Step-by-step explanation:

817

x 45

_______

+ 4085

+ 32680

__________

36,765

5 0

3 years ago

Read 2 more answers

The calibration of a scale is to be checked by weighing a 13 kg test specimen 25 times. Suppose that the results of different we

Natali5045456 [20]

Solution :

a).

Given : Number of times, n = 25

Sigma, σ = 0.200 kg

Weight, μ = 13 kg

Therefore the hypothesis should be tested are :

$H_0 : \mu = 13$

$H_a : \mu \neq 13$

b). When the value of $\overline x = 12.84$

Test statics :

$Z=\frac{(\overline x - \mu)}{\frac{\sigma}{\sqrt n}}$

$Z=\frac{(14.82-13)}{\frac{0.2}{\sqrt {25}}}$

$=\frac{1.82}{0.04}$

= 45.5

P-value = 2 x P(Z > 45.5)

= 2 x 1 -P (Z < 45.5) = 0

Reject the null hypothesis if P value < α = 0.01 level of significance.

So reject the null hypothesis.

Therefore, we conclude that the true mean measured weight differs from 13 kg.

3 0

3 years ago

Answer this question. (5.6)(1.8)

OverLord2011 [107]

(5.6)(1.8) the answer is 10.08

4 0

2 years ago

Read 2 more answers

Mary wants to make 20 gallons of a 52% acid solution by mixing together a 84% acid solution and a 4% acid solution. How much of

Setler [38]

Answer:

12 gallons 84%
8 gallons 4%

Step-by-step explanation:

I like to use an "X-diagram" to solve mixture problems. On the left side are the constituents of the mix; in the middle is the result of the mix; and on the right side are the differences between the numbers on each diagonal. These differences are the ratio numbers for the mix.

Here, that means the ratio of 84% solution to 4% solution is ...

48 : 32 = 12 : 8

Note that the last two "ratio numbers" were chosen so their sum is 20, hence they represent the number of gallons of the corresponding constituent in the mix. (The sum of the first two ratio numbers is 48+32=80, so to get a sum of 20, we divide each by 4.)

Mary must use ...

12 gallons of 84% acid solution
8 gallons of 4% acid solution

You may note that this solution takes much longer to explain than to do. The math here can all be done without a calculator.

_____

<em>Check</em>

12 × 84% + 8 × 4% = 10.40 = 20 × 52%

_____

<em>Usual Solution</em>

A more conventional approach would be to assign x to the amount of 84% solution needed. Then the number of gallons of acid in the mix is ...

0.84x + 0.04(20 -x) = 0.52(20)

0.80x + 0.8 = 10.4 . . . . simplify

0.80x = 9.6 . . . . . . . . . . subtract 0.8; next, divide by 0.8

x = 9.6/0.8 = 12 . . . . gallons of 84% acid

20-x = 8 . . . . . . . . . . gallons of 4% acid

3 0

3 years ago

A parabola can be represented by the equation x2 = -20y.

aliya0001 [1]

Answer:

$\mathrm{Parabola\:focus\:given}\:x^2=-20y:\quad \left(0,\:-5\right)$

Step-by-step explanation:

Given the equation

$x2 = -20y$

A parabola is the locus of points such that the distance to a point the focus equals the distance to a line the directrix.

$4p\left(y-k\right)=\left(x-h\right)^2$ is the standard equation for an up-down facing parabola with vertex at (h, k), and a focal length |p|.

so

$x^2=-20y$

$\mathrm{Switch\:sides}$

$-20y=x^2$

$\mathrm{Factor\:}4$

$4\cdot \frac{-20}{4}y=x^2$

$4\left(-5\right)y=x^2$

$\mathrm{Rewrite\:as}$

$4\left(-5\right)\left(y-0\right)=\left(x-0\right)^2$

$\left(h,\:k\right)=\left(0,\:0\right),\:p=-5$

Parabola is symmetric around the y-axis and so the focus lies a distance\ p from the center (0, 0) along the y-axis.

$\left(0,\:0+p\right)$

$=\left(0,\:0+\left(-5\right)\right)$

$\mathrm{Refine}$

$\left(0,\:-5\right)$

Therefore,

$\mathrm{Parabola\:focus\:given}\:x^2=-20y:\quad \left(0,\:-5\right)$

Please check the attached figure too.

6 0

3 years ago

Read 2 more answers