When Mike's phone is fully charged, it runs out in 32 hours if he uses it only for phone calls, in 20 hours if he only uses it for the internet, and in 80 hours if he does not use it at all. Mike gets on a train with his phone half charged. While on the train, the time he is on the internet, the time he is making phone calls, and the time he is not using it are all the same. His phone runs out of charge just as the train reaches his destination. How many hours did the train journey take? Let's say that this journey took x hours. It tells us that he uses his phone for an equal number of hours on each part of the journey and therefore he spends x over 3 hours on each of the 3 activities. Each time he makes a phone call, he uses 1 out of 32 of his battery per hour because his phone runs out in 32 hours if he uses it only for phone calls. We can similarly determine that if he uses 1 out of 20 of his battery per hour using the internet and 1 out of 80 of his battery per hour when he is not using it. Then we know that he uses 1 out of 32 plus 1 out of 20 plus 1 out of 80 times x over 3 of his phone battery during the trip because that is the rate of his usage times the time he used it for. We know that he started with his phone charged so we can solve our equation of what we just determined equals 1 half and solving for that we get x equals 16 and therefore our correct answer is D.

train journey

battery depletion

phone usage

equation solving

16 hours