David travels from home to work at 30 mph. At the end of the day, he travels from work back home via the same route at 40 mph. What is his average speed while travelling? (Give your answer as a simplified fraction) (None-Calculator)

First set the distance between home and work as the value x miles.The time takento get from home to work is the value y hours.The time takento get from work to home is the value z hours.Then (as timeis equal to distance divided by speed),x/30 = yandx/40 = z
The averagespeed while travelling can be calculated by taking the total distance travelled(2x miles) divided by the total time taken (y+z hours). Therefore,(Average speed)= (2x)/(y+z)Substituting yand z gives,(Average speed)= (2x)/((x/30)+(x/40))=(2x)/((40x +30x)/(1200))= 2400x / 70x= 2400 / 70= 240 / 7
David's averagespeed while travelling is 240/7 miles per hour.