16. 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 current.

A. 1 km/hr B. 2 km/hr C. 3 km/hr D. 4 km/hr

Answer Answer: Option A Explanation: First of all, we know that
speed of current = 1/2(speed downstream - speed upstream) [important]
So we need to calculate speed downstream and speed upstream first.
Speed = Distance / Time [important]
Speed upstream =(15334)km/hr=15×415=4km/hrSpeed Downstream = (5212)km/hr=5×25=2km/hrSo speed of current = 12(4−2)=1km/hr

19. 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)

20. A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in 6 1/2 hours. the velocity of the current is?

A. 1 km/hr B. 1.5 km/hr C. 2 km/hr D. 2.5 km/hr

Answer Answer: Option C Explanation: Let rate upstream = x km/hr and rate downstream =y km/hr.
Then, 24/x+36/y =36 ...............(1) and 36/x+24/y = 13/2 ...............(2)
Adding (1) and (2) we get : 60(1/x+1/y) = 25/2 or 1/x+1/y = 5/24 ....................(3)
subtracting (1) from (2) we get :12(1/x-1/y) =1/2 or 1/x-1/y=1/24 .....................(4)
Adding (3) and (4) we get : 2/x = 6/24 or x =8.
so, 1/8+1/y =5/24 <=> 1/y = (5/24-1/8) = 1/12 <=> y =12.
therefore speed upstream = 8 km/hr, speed downstream = 12 km/hr.
Hence, rate of current = 1/2(12-8) km/hr = 2 km/hr.