The description says:
Olivia and John lives 150km from each other. They want to meet in a place in the middle. Olivia thinks she can drive the whole distance in 3 hours. She drives from home at 12:00. John doesn't trust his vehicle, so he thinks he needs 5 hours driving 150km. He leaves home at 13:00. How far is the meeting point from where Olivia lives?
I don't understand this task so I don't know how to set up the equations. Is this a strange task, or does it makes sense? Why would he leave one hour later than her if he thinks he will spend two hours more for example, but that's perhaps not relevant..
I think the time at which they leave is not related to how much they trust their vehicle. There are some assumptions to be made to get to an answer though.
Say Olivia and John do drive their predicted average speed until they meet each other. Then the average speed of Olivia equals $v_o = \frac{150}{3} = 50 \frac{km}{h}$ and Johns avarage speed equals $v_j = \frac{150}{5} = 30 \frac{km}{h}$.
The final piece of the puzzle is to connect this to the time they are leaving. At first only Olivia is driving, so they are getting closer at a speed of $50 km/h$. After one hour (50km is covered), they get closer at $80 km/h$. Mathematically: $$ 150 = 50(t+1) + 30t$$ So $t=\frac{5}{4}$, one hour and 15 minutes, the time that John drives. In that time John is driven $37,5 km$. Olivia has driven 2 hours and 15 minutes and has covered $112,5 km$, which makes sense!