A-Kira-and-Kevin Problem

This is one of those Kira and Kevin problems found in the Exam MLC Actuarial Models. This particular question really pissed me off the first time I tried it because it took me a looong time to solve. This is easy though, if you are familiar with the concept of a joint-life status.

Kevin and Kira excel at the newest video game at the local arcade, "Reversion". The arcade has only one station for it. Kevin is playing. Kira is next in line. You are given:

1. Kevin will play until his parents call him to come home.
2. Kira will leave when her parents call her. She will start playing as soon as Kevin leaves if he is called first.
3. Each child is subject to a constant force of being called: 0.7 per hour for Kevin; 0.6 per hour for Kira.
4. Calls are independent.
5. If Kira gets to play, she will score points at a rate of 100,000 per hour.

Calculate the expected number of points Kira will score before she leaves.