Idont have much time.

frederick headed for lutzen at 3 kph. later he increased his speed to 4 kph. if it was 52 kilometers to lutzen and the total time of travel was 15 hours, how long did he travel at 3 kph?

Since distance is equal to rate times time:

Let x= the time traveled at 3 km/h

Let y= the time traveled at 4 km/h

We can say that

3x+4y=52

Or that three (kilometers) times the time traveled at 3 kilometers an hour plus 4 (kilometers) times the time traveled at 4 kilometers an hour is equal to 52; the total distance traveled.

Likewise, we can see that:

x+y=15

Because x, the number of hours traveled at 3 km/h added to y, the time traveled at 4 km/h is equal to 15; the total time traveled.

Now, I'll solve by substitution.

x=-y+15

Substitute that into the other equation.

3(-y+15) + 4y = 52

Distribute

-3y + 45 + 4y = 52

Combine like terms

y + 45 = 52

Minus 45 from both sides

y = 7

So Fredrick traveled at 4 km/h for 7 hours.

Now, to find the other value, substitute the value of y into one of the original equations.

x + 7 = 15

Minus 7

x = 8

So

Time traveled at 4 km/h = 7 hours

Time traveled at 3 km/h = 8 hoursSince distance is equal to rate times time:

Let x= the time traveled at 3 km/h

Let y= the time traveled at 4 km/h

We can say that

3x+4y=52

Or that three (kilometers) times the time traveled at 3 kilometers an hour plus 4 (kilometers) times the time traveled at 4 kilometers an hour is equal to 52; the total distance traveled.

Likewise, we can see that:

x+y=15

Because x, the number of hours traveled at 3 km/h added to y, the time traveled at 4 km/h is equal to 15; the total time traveled.

Now, I'll solve by substitution.

x=-y+15

Substitute that into the other equation.

3(-y+15) + 4y = 52

Distribute

-3y + 45 + 4y = 52

Combine like terms

y + 45 = 52

Minus 45 from both sides

y = 7

So Fredrick traveled at 4 km/h for 7 hours.

Now, to find the other value, substitute the value of y into one of the original equations.

x + 7 = 15

Minus 7

x = 8

So

Time traveled at 4 km/h = 7 hours

Time traveled at 3 km/h = 8 hours

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x