Answer:
5.43 miles
Explanation:
Required
Determine the distance from school to her home
Given.
[When going to school]
[tex]Speed = 6mph[/tex]
Represent time with t
Distance is calculated as:.
[tex]Distance = Speed * Time[/tex]
[tex]Distance = 6 * t[/tex]
[tex]Distance = 6t[/tex]
[When coming back from school]
[tex]Speed = 35mph[/tex]
[tex]Time = \¾\ hour\ lesser[/tex]
This implies that she spends t - ¾hr when coming back from school.
So,
[tex]Distance = Speed * Time[/tex] becomes
[tex]Distance = 35 * (t - \¾)[/tex]
[tex]Distance= 35(t - \¾)[/tex]
[Equate both expressions of distance]
[tex]35(t - \¾) = 6t[/tex]
[Open Bracket]
[tex]35t - 35 * \¾ = 6t[/tex]
[tex]35t - 26.25 = 6t[/tex]
[Collect like terms]
[tex]35t - 6t = 26.25[/tex]
[tex]29t = 26.25[/tex]
[Solve for t]
[tex]t = \frac{26.25}{29}[/tex]
[tex]t =0.91[/tex]
[Substitute 0.91 for t in]
[tex]Distance = 6t[/tex]
[tex]Distance = 6 * 0.91[/tex]
[tex]Distance = 5.43\ miles[/tex]
Hence, the school is 5.43 miles from her home
