Question

Herman is traveling 125 miles from his house to the beach by car. Herman plans to stop for lunch when the ratio of the distance he has traveled to the distance he still has to travel is 2:3. What distance will Herman have traveled when he stops for lunch?

Answer 1

Answer:

250 miles

Step-by-step explanation:

The given distance between the house and the beach is 125 miles.

Let $x$ miles be the distance between the house and the lunch stop.

So, at the time of the lunch stop, he already traveled $x$ miles, the remaining distance is the distance between the lunch stop and the beach.

Let $y$ miles be the remaining distance, so

$y=125-x.$

Give that the ratio of the distance he has traveled, $x$, to the distance he still has to travel, $y$, is $2:3$,i.e

$x:y=2:3$

$\Rightarrow \frac x y =\frac 2 3$

$\Rightarrow \frac {x}{125-x}=\frac 2 3$

$\Rightarrow 3\times x=2\times(125-x)$

$\Rightarrow 3\times x=2\times125-2\timesx$

$\Rightarrow 3 x=250-2x$

$\Rightarrow 3x-2x=250$

$\Rightarrow x=250$

Hence, the distance traveled by Herman when he stops for lunch is 250 miles.