Let the length of the journey be $x$ km.

Recall that speed MATH

So time MATH.

We must use the same time units throughout. We will use hours.

Now 50 minutes MATH hours

In the forward journey, the car's time was $\dfrac{x}{30}$ hours.

For the return journey, the time was $\dfrac{x}{40}$ hours.

The total time was MATH hours.

So MATH

This gives us MATH

That is MATH

So the distance from home to work is $14.3$ km.