The table is an illustration of distance, rates (speed) and time.
- The best equation to solve for x is: [tex]\frac x8 + \frac x{16} = \frac 34[/tex].
- Gerry lives 4 miles from school
From the question, we have:
[tex]t =45\ mins[/tex] --- total time spent
Convert to hours
[tex]t =\frac{45}{60}hr[/tex]
Reduce fraction
[tex]t =\frac{3}{4}hr[/tex]
The times spent to school and back home are given as:
[tex]t_1 = \frac x8[/tex]
[tex]t_2 = \frac x{16}[/tex]
So, we have:
[tex]t_1 + t_2 = t[/tex]
This gives:
[tex]\frac x8 + \frac x{16} = \frac 34[/tex]
Hence, the equation that can be used to solve for x is: [tex]\frac x8 + \frac x{16} = \frac 34[/tex]
Take LCM
[tex]\frac{2x + x}{16} = \frac 34[/tex]
[tex]\frac{3x}{16} = \frac 34[/tex]
Multiply through by 16
[tex]\frac{3x}{16}\times 16 = \frac 34 \times 16[/tex]
[tex]3x = 12[/tex]
Divide both sides by 3
[tex]x = 4[/tex]
The distance to school and back home are given as:
[tex]d_1 = d_2 = x[/tex]
So, we have:
[tex]d_1 = d_2 = 4[/tex]
This means that Gerry lives 4 miles from school
Read more about distance, rates and time at:
https://brainly.com/question/1090517
