Lara and Tim took different routes to travel from Point A to Point C. Lara took the route along A, B, and C. Tim took the route along A, E, D, and C. Their routes with distances and times are shown. Which person's average speed is greater?

Tim's average speed is greater

Explanation:

Lara traveled a total distance of

AB+BC = (6 miles)+(2 miles) = 8 miles

and did so in

(1.5 hours)+(1 hour) = 2.5 hours

Plug those values into the formula

r = d/t

and we get

r = (8 miles)/(2.5 hours)

r = (8/2.5) mph

r = 3.2 mph

Lara's average speed is 3.2 mph

We'll follow the same steps for Tim as well

total distance = AE+ED+DC

total distance = (2 mi)+(4 mi)+(6 mi)

total distance = 12 miles

total time = (0.5 hr)+(1.5 hr)+(1.5 hr)

total time = 3.5 hours

rate = distance/time

r = d/t

r = (12 miles)/(3.5 hours)

r = (12/3.5) mph

r = 3.42857 mph approximately

Tim's average speed is roughly 3.42857 mph. We see that he has the greater average speed.