Fred takes his geocaching very seriously. He has found out that the time time it takes him to complete a cache from arriving at the parking place, finding the cache and returning to his car, can be modeled by a probability density function given by:
P(t)=ke-kt
Where t is the time in minutes that he takes to do a cache and k is a constant.
By integrating this function he can find the probability of finding a cache in a certain time. Fred knows that he completes 50% of his caches in 56 minutes and 13.8 seconds.
How long does it take Fred to complete 20% of his caches? This time is the Easting of the co-ordinates of the cache in minutes.
How long does it take Fred to complete 47.328% of his caches? This time is the minutes part of the Northing of the location of the cache. The Northing is given by 51 degrees and X minutes. X is the number you just found.