Question

The distance between 2 towns is 330km. A train travels between these two towns and returns on the same day. On the return journey, the train left late and so the driver decided to drive the train 5km/h fasterthan its inward journey, and it took 30 minutes less time to return. What is the speed on the return journey?

I used the folowing equation:

Let inward speed be x,

330/x - 330/x+5 = 1/2

However, I keep getting a squared x?

Answer 1

330/x - 330/(x+5) = 1/2

That's ok, we end up with a quadratic.
Multiply each term by 2x(x+5)
660(x+5) - 660x = x(x+5)
660x + 3300 - 660x = x^2 + 5x
x^2 + 5x - 3300 = 0
(x-55)(x+60) = 0
x = 55 or x = -60, we would reject the -60

So your inward speed is 55 km/h, the return is 60 km/h

check:
330/55 = 6 hrs
330/60 = 5.5 hrs, which is 1/2 hour less.

Answer 2

Thanks Reiny, appreciate it