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Blue Poster, Question 2

Travelling by Dart avoids the traffic. But what if you were driving and you calculate that you must achieve and average of 60 km/hr to make your destination on time? The traffic is heavier than anticipated but clears when you reach the half-way point where you realise you have only managed an average speed of 30 km/hr. What average speed would you have to drive for the remaining half of the journey to arrive on time?

Answer

This is a nasty trick – it is impossible to arrive on time.

If you are clever and you know that velocity = distance/time you can do the calculations and with a little bit of algebra, you will get the answer of infinity.

If you are really clever though, you wouldn’t bother with this because you would have spotted that your allotted time was used up at the halfway point.

If you drive at half the speed you will only get half as far in the allotted time, therefore your time is used up at the halfway point.

Another way of approaching it is to use some real values. Say you need to drive at 60 km/h for one hour to arrive on time. That means it is a distance of 60 km. If you only manage to do half the speed (30km/h), for half the journey. That would be 30km you would have travelled. At 30km/h that would take you 1 hour. But that was your allotted time, so you couldn’t make it at any speed.