You are given a math word problem and you are supposed to make use of mathematical concepts like probability, combinatorics, linear equations, sequences/series, or simple operators like addition, subtraction, division, or multiplication to answer the given question. Choose the best option from the 5 given options and report that option.

Question: On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him?

 Option A: 1/4

 Option B: 4/5

 Option C: 1/5

 Option D: 1/6

 Option E: 1/7
Option E

Question: Car ‘X’ covers a distance of 385 kms in 7 hours and car ‘Y’ covers a distance of 715 kms in 13 hrs. What is the difference in the speed of the two cars?

 Option A: 2kms/hr

 Option B: 1km/hr

 Option C: 3kms/hr

 Option D: 5kms/hr

 Option E: None of these
Option E

Question: Only a single rail track exists between stations A and B on a railway line. One hour after the north bound super fast train N leaves station A for station B, a south-bound passenger train S reaches
station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day, N leaves for B from A, 20 min behind the normal schedule. In order to maintain the schedule, both N and S increased their speeds. If the super fast train doubles its speed, what should be the ratio (approximately) of the speeds of passenger train to that of the super fast train so that the passenger train S reaches exactly at the scheduled time at A on that day?

 Option A: 1 : 3

 Option B: 1 : 4

 Option C: 1 : 5

 Option D: 1 : 6

 Option E: 1 : 7

Option D