average speed over a set distance

[W Sussex Sue]

If you wanted to travel a set distance at an average speed of 60 mph, would you do it by
(a) travelling for half the time at 50 mph and half at 70 mph or,
(b) travelling half the distance at 50 mph and the other half at 70 mph ?

[Buenchico]

I think that this ought to be in 'Science' or 'How it Works' but, anyway, (a) is correct.

To see why (b) doesn't work, make the total distance 700 miles (to keep the sums easy). So 350 miles is travelled at 50mph (thus taking 7 hours) and another 350 miles is travelled at 70mph (thus taking 5 hours). Therefore 700 miles has been travelled in 12 hours, giving an average speed of 58.33mph (to 4 s.f).

To check that (a) works, simply make the total time travelled equal to 2 hours. So the first hour is at 50mph (meaning 50 miles has been travelled) and the second hour is at 70mph (meaning 70 miles has been travelled). Thus 120 miles has been travelled over 2 hours, which averages 60mph.

Chris

[sp1214]

To achieve an average speed of 60 mph in practice you would need to be travelling nearer to 68 mph most of the way. Have you seen those cameras on the motorway where there are no holdups but state the time to some distance ahead is calculated about 60 mph but where the speed limit is 70 mph.

[Toureman]

I agree with mdoo, on todays roads you would probably have to cruise at 120 MPH wherever you could to get anywhere near an average of 60MPH.