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 total 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.

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.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

answer: rolling a number cube and flipping a coin.

step-by-step explanation: