Samantha’s car broke down when she was on a road trip. The nearest town, Buckville, was 10 miles away, and her phone had no service, sho she couldn’t call for help. She decided to start walking to Buckville. She walked directly towards the town for an hour at a rate of 2mph when she realized she had left her wallet at the car. Knowing she’d need it to get help, she turned around and started speedwalking back to the car at a rate of 4mph. She reached her car, grabbed her wallet, and then started the journey back to Buckville. She jogged the whole way there at a rate of 5mph. 1. How much time did it take for Samantha to realize she’d forgotten her wallet? 2. How much time did it take for Samantha to get back to her car to get her wallet? 3. How much time did it take Samantha to get back to Buckville after she’d retrieved her wallet? 4. Overall, how much time did it take for Samantha to get back to Buckville?5. What’s the furthest distance Samantha was from Buckville? 6. How far did Samantha actually travel in her journey to Buckville?

Accepted Solution

1. The problem statement tells you it took 1 hour for Samantha to realize she forgot her wallet.

2. Samantha speed-walked back to the car at twice the speed she was originally walking, so it took her half the time, 1/2 hour.

3. Samantan jogged the 10 mile distance at 5 miles per hour. It took her
  (10 mi)/(5 mi/h) = 2 h
to get to Buckville.

4. Assuming you want the total time it took Samantha to get to Buckville, it would be
  (1 h) +(1/2 h) +(2 h) = 3 1/2 hours

5. Samantha was farthest from Buckville when she was at her car, a distance of 10 miles from Buckville.

6. At 2 miles per hour, the hour Samantha initially walked toward Buckville took her 2 miles. She retraced that 2 miles, then jogged 10 miles, for a total of ...
  2 mi +2 mi +10 mi = 14 miles