Answer:
250 miles
Step-by-step explanation:
The given distance between the house and the beach is 125 miles.
Let [tex]x[/tex] miles be the distance between the house and the lunch stop.
So, at the time of the lunch stop, he already traveled [tex]x[/tex] miles, the remaining distance is the distance between the lunch stop and the beach.
Let [tex]y[/tex] miles be the remaining distance, so
[tex]y=125-x.[/tex]
Give that the ratio of the distance he has traveled, [tex]x[/tex], to the distance he still has to travel, [tex]y[/tex], is [tex]2:3[/tex],i.e
[tex]x:y=2:3[/tex]
[tex]\Rightarrow \frac x y =\frac 2 3[/tex]
[tex]\Rightarrow \frac {x}{125-x}=\frac 2 3[/tex]
[tex]\Rightarrow 3\times x=2\times(125-x)[/tex]
[tex]\Rightarrow 3\times x=2\times125-2\timesx[/tex]
[tex]\Rightarrow 3 x=250-2x[/tex]
[tex]\Rightarrow 3x-2x=250[/tex]
[tex]\Rightarrow x=250[/tex]
Hence, the distance traveled by Herman when he stops for lunch is 250 miles.
