Question

Amy and Beth live the same place which is 10 miles from the grocery store. Amy gets in her car and drives to the store at 30 miles per hour. At the same time Amy starts driving, Beth starts walking toward the store at 3 miles per hour. Amy spends 1 hour at the store, and then drives home at 30 miles per hour. How many miles away from home will Amy and Beth meet? Express your answer as a fraction.

Answer 1

it takes Amy 1/3 hr to get to the store.
Another hour passes.

During that time, Beth has walked 1+3 = 4 miles.

So, the two must cover 26 miles at a combined rate of 30+3=33 mi/hr.

That takes 26/33 hours.

During that time, Beth has walked another 26/33*3 = 26/11 miles.

So, they meet 4 + 26/11 = 70/11 miles from home.