Eudora ran from her home to her secret laboratory at an average speed of 12 km/h she then took one of her jetpacks and flew to her school at an average speed of 76 km/h eudora traveled a total distance of 120 kilometers, and the entire trip took 2 hours. how long did eudora spend running, and how long did she spend flying using her jetpack?

She spent 0.5 hrs running to her secret laboratory and 1.5 hrs flying using her jetpacks.

Step-by-step explanation:

Eudora ran from her home to her secret laboratory at an average speed of 12 km/h. The journey with her jet pack to her school has an average speed of 76km/hr. Eudora traveled a distance of 120 kilometers.  This means the total journey when she ran and flew she could cover a distance of 120 km and the entire trip took 2 hours.

The trip can be categories into two

when she ran to her secret laboratory

Speed = 12 km/hr

let the time she ran to her  secret laboratory  = a

speed = distance /time

distance = speed × time

distance = 12 × a

distance = 12a

when she flew to her school

speed = 76 km/hr

The time she flew to her school = 2 - a

speed = distance /time

distance = speed × time

distance = 76 × 2 - a

distance = 152 - 76a

Total distance of her entire trip = 120 km

total time = 2 hrs

Total distance can be represented as

12a +  152 - 76a = 120

-64a = 120 - 152

-64a = -32

divide both side by -64

a = -32/-64

a = 0.5 hrs

she spent 0.5 hrs running to her secret laboratory

Time she flew with her jetpacks = 2 - a = 2 - 0.5 = 1.5 hrs  

faster, im not sure why but i know it is faster

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9