my brother and i walk the same route every day. my beother takes 40minutes to get to school and i take 30minutes to get to school. today my brother left 8minutes before me. how long will it take me to catch up? suppose my brother's headstart is 5 instead of 8 minutes. now how long will it take me to catch up?

In 1 minute, I walk = 1/30

In 1 minute, My brother walk = 1/40

In T minutes, I walk = T*1/30

My brother walk 8 minute before = T + 8

In 1 minute, My brother walk = (T + 8) * 1/40

When these two distances are same, then I will catch him.

T * (1/30) = (T + 8) * (1/40)

30 * (T + 8) = 40*T

30*T + 240 = 40*T

240 = 10*T

T = 24 minutes

hence, I will catch him in 24 minutes.

Take 5 instead of 8.

My brother walk 5 minute before = T + 5

In 1 minute, My brother walk = (T + 5) * 1/40

When these two distances are same, then I will catch him.

T * (1/30) = (T + 5) * (1/40)

30 * (T + 5) = 40*T

30*T + 150 = 40*T

150 = 10*T

T = 15 minutes

Hence, I will catch him in 15 minutes.