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

Answer:

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.

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

$\text{Your brother's speed}=\frac{D}{40}$

You take 30 minutes to get to school.

$\text{Your speed}=\frac{D}{30}$

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

$\frac{D}{40}\times (T+8)$

You speed: $\frac{D}{30}\times T$

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

$\frac{D}{40}\times (T+8)=\frac{D}{30}\times T$

Cross multiply:

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

Use distributive property:

$30DT+240D=40DT$

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

$240D=10DT$

Switch sides:

$10DT=240D$

$\frac{10DT}{10D}=\frac{240D}{10D}$

$T=24$

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