Travelling to some place and back again mightinvolve travelling twice the distance of only travelling there, butmight well not mean taking twice as long. Going in one directionmight mean travelling uphill or going against the wind or travellingin rush hour, meaning that this part of the total journey takeslonger.

To find a total time or the speed over one or bothparts of the journey can involve setting up an equation to be solved.

The distance from London toBrighton is 55 miles. The average speed from Brighton to London ismph and the average speed from London to Brighton ismph.The total travel time is 2 hours. Find

The Brighton to Londonjourney takeshours

The London to Brightonjourney takeshours.

The total journey takes 2hours so

We have to solve theequationWecan start by multiplying by toclear all the fractions, giving

ormph.The second of these is obviously wrong somph.