Answer
The distance between Bedingfield and Portsmouth is 150 km
Work Step by Step
Let $t_1$ is the time in hrs going and $t_2$ is the time in hrs coming back.
Driving from Bedingfield to Portsmouth:
$\textbf{(1)}\hspace{0.5cm} d=100t_1$
Driving back:
$\textbf{(2)}\hspace{0.5cm} d=75t_2$
and, also:
$\textbf{(3)}\hspace{0.5cm} t_1+t_2=3.5$
From $\textbf{(1)}$ and $\textbf{(2)}$
$\textbf{(4)}\hspace{0.5cm} 75t_2=100t_1\Rightarrow t_1=\dfrac{3}{4}t_2$
From $\textbf{(3)}$ and $\textbf{(4)}$
$\dfrac{3}{4}t_2+t_2=3.5\Rightarrow 3t_2+4t_2=14\Rightarrow 7t_2=14\Rightarrow t_2=2$
Substitute in $\textbf{(3)}$
$t_1+2=3.5\Rightarrow t_1=1.5$
Substitute in $\textbf{(1)}$
$d=100t_1=100(1.5)=150km$
The distance between Bedingfield and Portsmouth is 150 km
