Question

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 4 minutes before I did. How long will it take me to catch up with him?

Answer 1

To catch up to your brother who has a 4-minute head start, it will take you 12 minutes.

Step-by-step explanation:

To determine how long it will take for you to catch up with your brother on the way to school, we need to consider the different walking speeds and the time advantage your brother has.

First, let's determine your walking speeds. If your brother takes 40 minutes to reach school and you take 30 minutes for the same route, then assuming you both walk at a constant speed, we can say that your walking speed is 4/3 times faster than your brother's speed because 40 minutes divided by 30 minutes equals 4/3.

Now, given that your brother has a 4-minute head start, let's calculate the time it takes for you to catch up to him:

1. Since your speed is 4/3 times that of your brother's, in every 4 minutes, you gain a 1-minute advantage over him because 4 minutes divided by (4/3) equals 3 minutes, which means you walk the same distance 1 minute faster.
2. Your brother's head start is 4 minutes, so you will catch up to him in 4 minutes * 3/1 = 12 minutes.

Therefore, it will take you 12 minutes to catch up with your brother.

Answer 2

24 minutes.

Step-by-step explanation:

Let D represent the distance from school to home and T represent time.

We have been given that your brother takes 40 minutes to get to school.

`\text{Speed}=\frac{\text{Distance}}{\text{Time}}`

`\text{Your brother's speed}=(D)/(40)`

You take 30 minutes to get to school.

`\text{Your speed}=(D)/(30)`

Your brother left 4 minutes before you did, so distance traveled by him would be:

`(D)/(40)* (T+8)`

You speed:
`(D)/(30)* T`

You will catch your brother, when both distances would be same:

`(D)/(40)* (T+8)=(D)/(30)* T`

Cross multiply:

`30D(T+8)=40DT`

Use distributive property:

`30DT+240D=40DT`

`30DT-30DT+240D=40DT-30DT`

`240D=10DT`

Switch sides:

`10DT=240D`

`(10DT)/(10D)=(240D)/(10D)`

`T=24`

Therefore, it will take you 24 minutes to catch up your brother.