A train runs 25 miles at a speed of 30 mph, another 50 miles at a speed of 40 mph, then due to repairs of the track travels for 6 minutes at a speed of 10 mph and finally covers the remaining distance of 24 miles at a speed of 24 mph. What is the average speed in miles per hour?

Explanation

Time taken in covering 25 miles at a speed of 30 mph
`"=50 minutes " (.:' "Time"="Distance"/"Speed")" `
Time taken in covering 50 miles at a speed of 40 mph
= 75 minutes
Distance covered in 6 minutes at a speed of 10 mph = 1 mile
Time taken in covering 24 miles at speed of 24 mph = 60 minutes.
Therefore, taking the time taken as weights we have the weighted mean as:

Weighted Mean, `barX_(W)=(sumWX)/(sumW)=(6,000)/(191)=31.41`
Average Speed = 31.41 mph.