# To travel from Singapore to Kuala Lampur, a distance of 390 km, a motorist finds that if he travels 6 km/h faster than his usual average speed, he... will take 15 minutes less to complete his usual journey. Calculate the usual average speed of the motorist.

The information in the problem involves two variables: the usual average speed v, and the usual time t.

so 390 km = v*t and,

390 km = (v + 6)(t - 15/60)

From the first equation, t = 390 / v.

Plugging that into the second equation, we have:

390 = (v + 6)(390/v - 15/60)

390 = 390 + 6*390/v - 15v/60 - 15*6/60

0 = 6*390 - 15v^2/60 - 15*6v/60

Using the quadratic equation, v = (-b +- sqrt(b^2-4ac))/2a

So v = -99.7936 and 93.7936 km/h

Clearly the physical answer in this case is v = 93.8 km/h, since we assumed that v was positive.

Approved by eNotes Editorial Team