On a recent trip to Florida we averaged 50 miles per hour On

On a recent trip to Florida, we averaged 50 miles per hour. On the return trip we averaged 60 miles per hour. What do you think the average speed of the trip to Florida and back was? Defend your position. Algebraically, determine the average speed of the trip to Florida and back.

Solution

Distance(d)=rate(r) times time(t) or d=rt and t=d/r
Time down=d/50
Time back=d/60
Average Speed equals total distance divided by total time
Total distance=2d
Total time=d/50+d/60 so
Average Speed=2d/(d/50+d/60)
DENOMINATOR: LCM is 300: (d/50+d/60)=(6d+5d)/300=11d/300 now we have
Average Speed=2d/(d/50+d/60) =2d/(11d/300)

Average Speed=2d(300/11d)=600/11=54.545 mph---------------------answer