Peter and his neighbor, Juan, walk 2 miles to school each day. Yesterday, Peter walked to school in 27 minutes. Juan walked the first mile to school in 11 minutes. If they leave at the same time today and maintain their rates from yesterday, what can you say about their arrival times?

Question

Peter will get to school first.
Juan will get to school first.
They will both arrive at school at the same time.

Answer 1

To determine their arrival times today, we first need to calculate their walking speeds based on their times from yesterday.

Peter's speed:

• Peter walked 2 miles in 27 minutes.
• His speed = Distance / Time = 2 miles / 27 minutes = \( \frac{2}{27} \) miles per minute.

Juan's speed:

• Juan walked the first mile in 11 minutes. Since the problem doesn't specify a different speed for the second mile, we can assume he walked the second mile in the same speed.
• His speed for the first mile = 1 mile / 11 minutes = \( \frac{1}{11} \) miles per minute.
• Assuming he maintains the same speed for the second mile, his total time for 2 miles would be 11 minutes + 11 minutes = 22 minutes.

Now we calculate the total times to arrive at school for both Peter and Juan:

• Peter's time yesterday for 2 miles:

  • 27 minutes.

• Juan's time yesterday for 2 miles:

  • 22 minutes.

Since they leave at the same time today and Juan's time is shorter, he will arrive first.

So the correct statement is: Juan will get to school first.