2. A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream.Find the speed of the river current in km/hr?

3. Two persons A and B start from the opposite ends of a 450 km straight truck and run to and from between the two ends. The speed of the first person is 25 m/s and the speed of other is 35 m/s. They continue their motion for 10 hours. How many times did they pass each other?

A. 1 B. 4 C. 3 D. 2

Answer Answer: Option D Explanation: First person speed = 25m/s *18/5 = 90 kmph.
Second person speed = 35m/s *18/5 = 126 kmph.
First person covers 90*10 = 900 km
900/450 = 2

4. At his usual rowing rate, A can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24 -mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. what is the speed of the current in miles per hour?

A. 1 1/3 B. 1 2/3 C. 2 1/3 D. 2 2/3

Answer Answer: Option D Explanation: Let the speed still in water be x mph and the speed of the current be y mph.
Speed upstream = (x-y): Speed downstream = (x+y)
12/(x-y) -12/(x+y) = 6 <=> 6(x^2 - y^2 = 24y ,<=> x^2-y^2 = 4y <=> x^2 = (4y+y^2)........(1)
And 12/(2x-y) - 12/ (2x+y) = 1 <=> 4x^2 - y^2 = 24y <=> x^2 = 24y+y^2/4 .........(2)

5. A man rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is?

A. 1 km/hr B. 1.5 km/hr C. 1.8 km/hr D. 3.5 km/hr

Answer Answer: Option A Explanation: Suppose he moves 4 km downstream in x hours. then,
speed downstream = (4/x) km/hr, speed upstream =(3/x) km/hr.
Therefore 48/(4/x) + 48/(3/x) =14
so speed downstream = 8 km/hr, speed upstream = 6 km/hr.
Rate of the stream = 1/2 (8-6) km/hr = 1 km/hr.