outward journey:
12 = (x + 7)( 1 - t) eq. 1.
ride back:
12 = (x)(t) eq .2.
• From eq 1:
12 = (x + 7)( 1 - t)
12 = x - tx + 7 - 7t eq. 3.
• Substituting eq. 2 on eq. 3:
[tex]\begin{gathered} 12=x-tx+7-7t \\ 12=\frac{12}{t}-t\frac{12}{t}+7-7t \\ 12=\frac{12}{t}-5-7t \\ t=\frac{4}{7} \end{gathered}[/tex]
• Substituting t on eq. 2:
[tex]\begin{gathered} 12=x\times t \\ x=\frac{12}{\frac{4}{7}}=21 \end{gathered}[/tex]
Rate while riding home = 21 mph
Rate outward journey = 28 mph
