My brother and I walk the same route to school every day. My brother takes 40 minutes to get to school and I take 30 minutes. Today, my brother left 8 minutes before I did. How long will it take me to catch up with him?
Let the distance to school S, my speed=S/30
the speed of my brother=S/40 and
I catch up with him after t min.
Then
S/40*(t+8)=S/30*t
30t+240=40t
To determine how long it will take you to catch up with your brother, we need to analyze the time difference between the two of you.
First, let's find out how long your brother will be walking alone before you start walking. Since your brother takes 40 minutes to get to school and left 8 minutes before you, we subtract 8 minutes from 40 minutes. This gives us 32 minutes, which is the head start your brother has.
Next, we need to calculate how much time you can "make up" on your brother's lead by walking faster. We know that you can walk to school in 30 minutes, while your brother takes 40 minutes. Therefore, you can make up 10 minutes for every 40 minutes of time.
Now, we can determine how long it will take you to catch up with your brother. Since your brother has a head start of 32 minutes and you can make up 10 minutes every 40 minutes, we can divide the head start by the time you can make up in 40 minutes.
32 minutes ÷ 10 minutes = 3.2 (rounded to the nearest whole number)
Therefore, it will take you approximately 3.2 intervals of 40 minutes to catch up with your brother. Multiplying this by 40 minutes gives us 128 minutes.
So, it will take you around 128 minutes to catch up with your brother.
To find out how long it will take for you to catch up with your brother, we need to determine the time difference between your starting points.
Since your brother left 8 minutes before you, he has a head start of 8 minutes.
Now, we need to calculate how long it takes for you to catch up with your brother based on the difference in your walking times.
The difference in your walking times is 40 minutes - 30 minutes = 10 minutes.
Therefore, it will take you 10 minutes to catch up with your brother.