A train goes from New Orleans to Boston at 40 mph. On the way back it returns with a speed 80 mph. If it takes it an hour less time to return, what is its average speed?

Distance from New Orleans to Boston and back is the same.

t - time from New Orleans to Boston

(t-1) - time from Boston to New Orleans

40t - distance between New Orleans and Boston.

80 (t-1) - distance between Boston and New Orleans.

40t = 80 (t-1)

40t = 80t - 80

40t = 80

t=2 h

To find average speed we need to find all distance and divide it at all time.

All distance = 40t + 80 (t-1) = 120t - 80

All time = t + (t-1) = 2t-1

Average speed = (120t - 80) / (2t-1)

Now we can substitute t=2.

Average speed = (120*2 - 80) / (2*2-1) = 53.33 m/s

Yes, it would be 53.33 miles per hour!