Answer: a.) 2/3 ; b.) 7/12
Step-by-step explanation:
Given the following details :
Destination A trains arrives at station at 15 minutes interval starting from 7am
Destination B trains arrives at station at 15 minutes interval starting from 7.05am
A.) if a passenger arrives at station uniformly between 7am and 8am and gets on first train. What proportion of time does the passenger leave from destination A?
To leave for destination A. The passenger has to arrive before train to A departs and after train to B leaves.
Train to B leaves, starting at at 7.05 a.m and at interval of 15 minutes
Train to A leaves at 7.00 am and at interval of 15 minutes.
Therefore,
(Train B departs - train A arrives) (between 7 to 8am)
(7.05 - 7.15) + (7.20 - 7.30) + (7.35 - 7.45) + (7.50 - 8.00) = 40 minutes
Total time = 7.00 - 8.00 = 60 minutes
(40 ÷ 60) = 2/3 or 0.667
B.) If passenger arrives uniformly between 7.10am - 8:10am
(7.10 - 7.15) + (7.20 - 7.30) + (7.35 - 7.45) + (7.50 - 8)
5 + 10 + 10 + 10 = 35
35/60 = 7/12 or 0.583
using pythagoras' theorem of 
. This gives us a value of 51m for the diagonal line.