Question

Walking at a speed of 3 mph, Jack gets to school in 10 minutes and arrives at school right before the class starts. Today Jack needs to be at school 4 minutes earlier. How fast does Jack need to run this morning?

A) 6 mph
B) 5 mph
C) 4 mph
D) 7 mph

Answer 1

Jack needs to run at a speed of 5 mph this morning.

Step-by-step explanation:

Let's analyze the problem step by step:

1. Jack currently walks to school at a speed of 3 mph. This means he covers a distance of 3 miles in 1 hour.
2. Jack arrives at school in 10 minutes, which is 10/60 = 1/6 hours. So, the distance from his home to school is 3 miles * (1/6) = 1/2 mile.
3. Now, Jack needs to be at school 4 minutes earlier. So, he needs to reduce his travel time from 10 minutes to 10 - 4 = 6 minutes.
4. To calculate the new distance he needs to cover, we'll use the formula:

Distance = Speed * Time

Since he still needs to cover the same distance from his home to school, we have:

1/2 mile = Speed * (6/60) hours
Speed = (1/2) mile / (6/60) hours

Calculating this expression gives us:
Speed = 5 mph

Therefore, Jack needs to run at a speed of 5 mph this morning.