Algebra 2 Math problem.. please help?

Question

ive been stuck on this problem for 2 hours..

an Elevator went from down to up of a building at an average speed of 6 m/s. The elevator stayed at the top of the building for 100 seconds and came back down at 8/m. If the total elapsed time was 380 seconds. How high is the building?

thnx soo much everyone

Answer 1

let the height be 'h' metres

h/6+h/8+100=380
h/6+h/8=280
14x/48=280
x=(48/14)*280
=960
the height ofthe building is 960m

Answer 2

You can solve this by understanding that distance = velocity x time

Or d = v x t

The elevator first goes up, but it doesn't tell us the height of the building or the amount of time it takes, so all we know is that

h = 6 x t1 (h is height, t1 is some amount of time)

Then the elevator sits at the top for 100 s, then comes back down. When it comes down, all we know is that

h = 8 x t2 (t2 is some other amount of time)

The distance up is the same as distance down, so we can say that the 2 equations are equal:

h = 6 x t1 = 8 x t2 solve this by dividing by 6 or 8

So t2 = (3/4) x t1

Now in 380s, the elevator goes up, sits for 100s, and comes down. The total TRAVEL TIME is 280 seconds, because for 100s the elevator wasn't moving. So the time for the elevator to go up and come down without resting is 280s.

The total travel time then: t1 + t2 =280

From the last set of equations, t2 = (3/4) x t1 and we substitute"

t1 + 3(t1 /4) = 1.75 x t1 = 280

t1 = 280s / 1.75 = 160s

Now from the first equation: h = 6 x t1 = 6 x 160s = 960 m

You can also solve this by finding t1 in terms of t2 and ultimately solving h = 8 x t2

You can solve for the height without finding the travel time but I think it is more difficult.

Answer 3

tot time = v1.t1 + v2.t2 + 100 = 6.t1 + 8.t2 + 100
t1 + t2 = 380 - 100 = 280s.
Since h = same both trips = v1.t1 = v2.t2 -> 6.t1 = 8.t2
Hence 6t1 = 8t2 or t2 = 6t1/8.
-> t1 + 6t1/8 = 280
-> t1 = 280 x 8 / 14 = 160s
(-> t2 = 280-160 = 120s not really needed)
Since h = v1.t1, we have h = 6x160 = 960m

Answer 4

to solve is a matter of substition in formulas

What do you know?

The height (h) can be expressed either as

h=6 m/sec * t1 (t1 the time to go up in elevator)
h=8 m/sec * t2 (t2 the time to go down)

You also know t1 sec + t2 sec +100 sec = 380 sec
t2 can be expressed as a parameter of t1, t2 = 280 sec - t1 sec

Since the height is the same going up or down

6 m/sec * t1sec = 8 m/sec * t2 sec

substitute for t2

6 m/sec * t1 sec = 8 m/sec * (280 sec - t1 sec)

expand the right side of equation

6 m/sec * t1 sec = (8 m/sec * 280 sec) - (8 m/sec * t1 sec)

re-arrrnage

(6 m/sec * t1 sec) + (8 m/sec * t1 sec) = (8 m/sec * 280 sec)

(6 m/sec + 8 m/sec) t1 sec = 2240 m

(14 m/sec)t1 sec = 2240 m

t1 sec = (2240 m )/ (14 m/sec)

the rest is simple math

knowing t1, you can determine t2,
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I carried the unit of measurement, always a nice check that the answer comes out in the right units

e.g d (m) = t (sec) * s (m/sec)
d (m) = t*s (m)

Answer 5

I got here up with an answer of 7x^2-3/(x-3)(x+3)(x+2) and my TI 89 concurs with my answer. First locate the liquid crystal show it fairly is (x-3)(x+3)(x+2) x^2-9 is a distinction of two squares that are (x-3)(x+3) so now you have 4x/(x-3)(x+3) because of the fact the 1st area of the subject.The denominator of the 2d area of the subject is a polynomial which could be factored into (x+3)(x+2). So now with the 2d area of the subject you have 3x+a million(x+3)(x+2) you presently might desire to positioned your liquid crystal show under the 4x and multiply it by technique of the (x+2) it fairly is lacking. next take the 3x+a million and place the liquid crystal show under it and multiply the numerator by technique of the lacking area of the liquid crystal show it fairly is (x-3). Now your subject might desire to look like 4x(x+2) + (3x+a million)(x-3) all divided by technique of the liquid crystal show of (x-3)(x+3)(x+2). next use the distributive sources for the 1st numerator and FOIL the 2d numerator and get carry of (4x^2 + 8x) + (3x^2 -9x + x -3) all divided by technique of the liquid crystal show of (x-3)(x+3)(x+2). next distribute the middle + time era and get 4x^2 + 8x + 3x^2 - 9x + x - 3. combine like words and get 4x^2 + 8x + 3x^2 - 8x -3. The 8x's cancel out and the x^2's combine to grant you 7x^2 - 3 all divided by technique of the liquid crystal show of (x-3)(x+3)(x+2)