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Eudora ran from her home to her secret laboratory at an average speed of 12\text{ km/h}12 km/h12, start text, space, k, m, slash, h, end text. She then took one of her jetpacks and flew to her school at an average speed of 76\text{ km/h}76 km/h76, start text, space, k, m, slash, h, end text. Eudora traveled a total distance of 120120120 kilometers, and the entire trip took 222 hours. How long did Eudora spend running, and how long did she spend flying using her jetpack? Eudora ran for hours and flew for hours using her jetpack.

Sagot :

MrRoyal

Answer:

Eudora spent 0.5 hours from home to library and 1.5 hours from library to school

Step-by-step explanation:

Given

Home to Library:

[tex]S_1 = 12km/h[/tex] -- Average Speed

Library to School

[tex]S_2 = 76km/h[/tex] -- Average Speed

Total

[tex]Distance = 120km[/tex]

[tex]Time = 2\ hr[/tex]

Required

Determine the time taken from home to library and from library to school

Let the time spent from home to library  be x. So, from library to school will be: 2 - x

So, we have:

Home to Library:

[tex]S_1 = 12km/h[/tex] -- Average Speed

[tex]T_1 =x[/tex] -- Time

Library to School

[tex]S_2 = 76km/h[/tex] -- Average Speed

[tex]T_2 =2 - x[/tex] -- Time

Distance is calculated as:

[tex]Distance = Speed * Time[/tex]

Home to Library:

[tex]D_1 = S_1 * T_1[/tex]

[tex]D_1 = 12 * x[/tex]

[tex]D_1 = 12x[/tex]

Library to School:

[tex]D_2 = S_2 * T_2[/tex]

[tex]D_2 = 76 * (2- x)[/tex]

[tex]D_2 = 152- 76x[/tex]

The total distance is 120km. So, we have:

[tex]120km = D_1 + D_2[/tex]

[tex]120 = 12x + 152 - 76x[/tex]

Collect Like Terms

[tex]120 - 152 = 12x - 76x[/tex]

[tex]-32 = -64x[/tex]

[tex]-64x=-32[/tex]

Solve for x

[tex]x = \frac{-32}{-64}[/tex]

[tex]x = 0.5[/tex]

Recall that:

[tex]T_1 =x[/tex]

[tex]T_2 = 2 - x[/tex]

So, we have:

[tex]T_1 = 0.5[/tex]

[tex]T_2 = 2 -0.5 = 1.5[/tex]

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