Respuesta :
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.
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
[tex]\text{Your brother's speed}=\frac{D}{40}[/tex]
You take 30 minutes to get to school.
[tex]\text{Your speed}=\frac{D}{30}[/tex]
Your brother left 4 minutes before you did, so distance traveled by him would be:
[tex]\frac{D}{40}\times (T+8)[/tex]
You speed: [tex]\frac{D}{30}\times T[/tex]
You will catch your brother, when both distances would be same:
[tex]\frac{D}{40}\times (T+8)=\frac{D}{30}\times T[/tex]
Cross multiply:
[tex]30D(T+8)=40DT[/tex]
Use distributive property:
[tex]30DT+240D=40DT[/tex]
[tex]30DT-30DT+240D=40DT-30DT[/tex]
[tex]240D=10DT[/tex]
Switch sides:
[tex]10DT=240D[/tex]
[tex]\frac{10DT}{10D}=\frac{240D}{10D}[/tex]
[tex]T=24[/tex]
Therefore, it will take you 24 minutes to catch up your brother.
