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]
