2 hours at 45 mph gives a distance of 90 miles he has another 90 miles to travel total distance=rate*(total time) his average speed must be 60 mph 180=60*(2+t) where t is the amount of time he has to travel the other 90 miles 180=120+60t 180-120=60t 60=60t t=60/60 t=1 hour Sam must travel 90 miles in 1 hour, thus Sam must travel 90 miles per hour to have an average of 60 mph 90 mph is the answer
you can check by using the harmonic mean if you understand what it is: (2*45*90)/(45+90)=8100/135=60
you can also find the answer using the harmonic mean: (2*45*R)/(45+R)=60 (2*45*R)=60*(45+R) 90R=2700+60R 90R-60R=2700 30R=2700 R=2700/30 R=90 mph must be Sam's speed for the other 90 miles to average 60 mph
