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.

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

To find out where Amy and Beth will meet, we need to determine how far each of them can travel during the one-hour period that Amy spends at the store.

Since Amy is driving at a constant speed of 30 miles per hour, she can travel 30 miles in 1 hour.

Beth, on the other hand, is walking at a constant speed of 3 miles per hour. Therefore, she can travel 3 miles in 1 hour.

So during the one-hour period, Amy travels 30 miles away from home to the store, and Beth travels 3 miles toward the store.

When Amy leaves the store, she needs to travel the same distance back home, which is another 30 miles. During this time, Beth continues walking at a constant speed of 3 miles per hour, so she covers an additional 3 miles.

Therefore, Amy and Beth will meet after Amy has driven 30 miles away from home and Beth has walked 6 miles toward the store.

Since they both started 10 miles away from the store, we need to find the remaining distance for both of them to meet.

For Amy, the remaining distance is 10 - 30 = -20 miles. However, distance cannot be negative, so we can disregard this value.

For Beth, the remaining distance is 10 - 6 = 4 miles.

Therefore, Amy and Beth will meet 4 miles away from home.

To express the answer as a fraction, we need to divide the remaining distance (4 miles) by the total distance they initially started from the store (10 miles), which gives us 4/10.

Therefore, Amy and Beth will meet 4/10 miles away from home, or simplified as 2/5 of a mile away.

Answer 2

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.