Sean drives from Manchester to Gretna Green. He drives at an average speed of 50 mph for the first three hours. He then breaks and drives the final 150 miles at 30 mph. Sean thinks his average speed is 40 mph ,is he correct?

This is a relatively complicated mechanics question requiring the student to put aside their initial assumption and work with the actual meaning of average speed. In order to do this the student must find out the total distance travelled and the total time it took and then work out average speed and compare it to Sean's answer. First it is necessary to state the formula; Average speed= Total distance travelled/Time taken. This can be rearranged to help us find the distance travelled : Total distance travelled= Average speed X time taken. As we already know that the final distance was 150 miles we only need to calculate for the first portion of his journey. This gives us the simple calculation of 50mph X 3 hours = 150 miles. This added to the second half of the journey means we now know the total journey from Manchester to Greta Green was in total 300 miles.We must now consider the total time taken. The formula needed can be obtained again by rearranging to; Time taken= distance/speed. This leads again to the relatively simple calculation of 150miles/30mph=5 hours. This means in addition to the first 3 hours the journey from Manchester to Gretna Green took 8 hours.We now have all the information needed to work out his average speed for the entire journey. We use the original formula; Average speed= Total distance travelled/Time taken. Plugging in all the numbers gives us the calculation 300miles/8hours= 37.5mph. This means Sean's actual average speed was lower than the 40 mph he estimated