Question

What was the average speed if I drove 60 miles per hour to get to my grandmas house and 30 miles per hour to get home. Represent this in two different ways and explain your reasoning.

Answer 1

40 mph.

Explanation:

Suppose grandma's house is 30 miles away (any distance would do but 30 is convenient).

Speed = distance / time

time = distance / speed

Time to get there = 30/60 = 1/2 hour.

Time to get back = 30/30 = 1 hour

Average speed = total distance/ total time

= (30 + 30) / ( 1 + 1/2)

= 60 / 1.5

= 40 miles per hour.

You cannot take the average of the speeds directly

(60+ 30)/2 = 45 is not correct as you cannot average ratios ( speed is a ratio).