Expert: Scott A Wilson - 9/10/2009

Question
A man travels 108km at a constant speed and finds he could have made the journey 4.5 hours shorter if he had travelled 2km/h faster. What was his speed.

I know the answer is 6km/h but i need to know how to do it. Have an exam tomorrow, you would be a life saver.

Answer
If he had gones at 6kph, it would be 18 hours.
If he had gone two faster, at 8kph, it would have been 13.5.

Let x be the speed.  The time is 108/x.
His new speed is x+2.  The new time is 108/(x+2).

We want 4.5 + 108/(x+2) = 108/x.  Multiply each term by x(x+2).
This works out to 4.5(x+2)x + 108x = 108(x+2).  Multiply out all terms to drop parenthesis.
That works out to 4.5x² + 9x + 108x = 108x + 216.  Move all terms to the left side.
That works out to 4.5x² + 9x - 216 = 0.
(-b±√(b²-4ac))/(2a) gives (-9±√(81+4(972))/9) = (-9±√3969)/9 = (-9±63)/9 = -1±7.
-1+7 = 6.  That's how I got there.