[hender]

A man wants to travel 3 miles at an average speed of 60 miles per hour. He has already trvelled half the distance at 30 mph. at what speed does the man need to travel to reach an average speed 0f 60 mph over the next half of his journey.

My friends say he cant. My theory is over the 2nd half he has to make up the 30 mph he's lost + his intended speed, therefore if he did 90 mph then he would average 60 mphn over the total distance.

If the man can't achieve an average speed of 60 what would be the closest he could get to it?

[Capuchin]

Sorry but your friends are right!

In order to average 60mph, he would need to travel the 3 miles in 3 minutes. However he's already taken 3 minutes to travel half the distance at 30mph! To average 60mph he would need to be at the end of the journey already.

I used to have a lot of trouble with why your logic in your answer is wrong. The reason is that the average speed is the average over time, not over distance. So travelling half of a journey at 30mph and half of a journey at 90mph does not average to 60mph. It averages to 45mph because you spend more time at 30mph.

In order to average 60mph at your speeds he would need to travel at 30mph for the first 1 1/2 minutes, and then 90 for the last 1 1/2 minutes. The distances covered being 1/4 and 3/4 of the total respectively. So your logic is nearly right, you just need to be careful in dealing with distance or time in future.