At home, Alice noticed that she had a flat tire. With the spare, Alice drove 30 miles to the next shop at 45 mph. After getting the new tire, she drove home at 70 mph. What was Alice's average speed for her round trip?

Approximately 54.7826 mph

As a fraction, this average speed is exactly 1260/23 mph.

Work Shown:

"Alice drove 30 miles...at 45 mph". This means

t = d/r

t = 30/45

t = 2/3

She drove for 2/3 of an hour, which is (2/3)*60 = 40 minutes.

Then "she drove home at 70 mph". She drove the same distance, meaning,

t = d/r

t = 30/70

t = 3/7

She drove for 3/7 of an hour, which is roughly (3/7)*60 = 25.714 minutes.

Add up the time values

(2/3 hr) + (3/7 hr)

(2/3 + 3/7) hr

(14/21 + 9/21) hr

23/21 hr

She spent 23/21 of an hour driving going to the auto shop and then back home. The total distance she traveled was 30+30 = 60 miles.

Use these values to find the speed

r = d/t

r = d divided by t

r = 60 divided by (23/21)

r = (60/1) divided by (23/21)

r = (60/1) * (21/23)

r = (60*21)/(1*23)

r = 1260/23

r = 54.7826

Her average speed for the round trip is about 54.7826 mph.

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