You and your brother both leave your house at the same instant and drive in separate cars along a straight highway to a nearby lake. After \(10 \mathrm{~min}\), you are both \(3.0 \mathrm{~km}\) from your house. You are now driving at \(100 \mathrm{~km} / \mathrm{h}\), and you continue at this constant speed; your brother is going faster than this. After another \(20 \mathrm{~min}\), your brother arrives at the lake, but you are still \(5.0 \mathrm{~km}\) away.

(a) How far is it from your house to the lake?

(b) What is your brother's average speed for the trip?

(c) Your brother beats you to the lake by what time interval?