Help with Math?

Question

a. Find the lowest common denominator (LCD)

3x/x^2+5x-24 , x+1/x^2-12x+27

b. A local bus travels 7 miles per hour slower than the express. The express travels 45 miles in the time it takes the local to travel 38 miles. Find the speed of each bus.

Thanks

Answer 1

a.) The denominators are (x + 8)(x - 3) and (x - 9)(x - 3)
So (x - 3)(x + 8)(x - 9) is the LCD.

b.) Let the speed of the express bus be x and the speed of the local bus be (x - 7).
Time taken is the same.
38/(x - 7) = 45/(x)
38x = 45x - 315
7x = 315
x = 45

Express --- 45 mi/hr
Local bus --- 38 mi/hr

Answer 2

factor denominators:
x² + 5x - 24 = (x+8)(x-3)
x² - 12x + 27 = (x-9)(x-3)

so LCD is (x+8)(x-9)(x-3)

let x be the speed of the local bus, x+7 the speed of the express. times are equal, time is distance divided by speed, so

45/(x+7) = 38/x ....... cross multiply
45x = 38(x+7)
45x = 38x + 38(7)
7x = 38(7)
x = 38 mph
x+7 = 45 mph.

Answer 3

x^2+5x-24
=(x+8)(x-3).
x^2-12x+27
=(x-3)(x-9).
LCM of (x^2+5x-24 &(x^2-12x+27)
=(x-3)(x+8)(x-9). ANS.
2.Let the speed of the express bus be emph, then the speed of the local bus=(e-7)Mph
then
45/e=38/(e-7)
45e-315=38e
7e=315
e=45 mph=speed of express bus.
speed of local bus=38MPH.

Answer 4

1). . . x^2

2) let B & E are the rates of Bus and Express respectively
B = E - 7 . . . . . equation 1
. . . . . time of bus = time of express
38/B = 45/E
B = 38/45 E . . . . . equation 2 . . substitute to equation 1
E - 7 = 38/45 E
7/45 E = 7
E = 45(7) / 7 = 45 mi/hr
B = 38 mi/hr

Answer 5

homework, aye? hahahha all we're doing in school is coloring and i'm in 7th grade honors. lol lol lol at u

Answer 6

woah