Time and Distance – Boats

1. A boat takes 4hours for traveling downstream from point P to point
   Q and coming back to point P upstream. If the velocity of the stream is 2km
   ph and the speed of the boat in still water is 4kmph, what is the distance
   between P and Q?A.9 km
   B.7 km
   C.5 km
   D.6km
   
   Answer

   Answer- D
   Basic Formula:
   Speed of stream = ½ (a-b) km/hr
   Speed of still water = ½ (a+b) km/hr
   Explanation:
   Time taken by boat to travel upstream and downstream = 4 hours
   Velocity of the stream, ½ (a-b) = 2km/hr
   a-b = 4km/hr ……………….( 1)
   velocity of the boat in still water = ½ (a+b) = 4km/hr
   a+b = 8 km/hr ………………(2)
   1 +2 we get a = 6 km/hr ,b = 2km/hr
   let the distance between A and B be x km
   x / 2 + x / 6 = 4
   3x + x / 6 = 4  4x = 24 so,x = 6
   distance between P and Q = 6km

2.Speed of a boat in standing water is 9kmph and the speed of the
stream is 1.5kmph. A man rows to a place at a distance of 10.5 km and
comes back to the starting point. Find the total time taken by him.A.24 hours
B.16 hours
C.20 hours
D.15 hours

Answer

Answer- A
Basic Formula:
i. speed = distance traveled / time taken
ii. speed of the stream = ½ (a-b) km/hr
iii. speed in still water = ½ (a+b) km/hr
Explanation:
Speed in still water= ½ (a+b) = 9km ph
= a+b = 18 …………….1
speed of the stream = ½ (a-b) = 1.5 kmph
= a-b = 3 kmph…………2
solving 1 and 2 gives a = 10.5km/hr ; b=7.5 kmphr
Total time taken by him = 105/10.5 + 105/7.5 = 24 hours

3.A man rows to a place 48km distant and back in 14 hours. He finds
that he can row 4km with the stream in the same time as 3km against the
stream. Find the rate of the stream.A.2 km/hr
B.1.1km/hr
C.3 km/hr
D.3.5km/hr

Answer

Answer- B
Basic Formula:
Speed of the stream = ½ (a-b) km / hr
Speed = distance traveled / time taken
Explanation:
Suppose he moves 4km downstream in x hours
Then, downstream a= 4 / x km/hr
Speed upstream b = 3/ x km/hr
48 / 4 /x + 48 / 3/x = 14
x/4 + x/3 = 14/48 = 1/4
3x + 4x / 12 = 1/4
7x x 4 = 12 so,x = 3/7
a=28/3 km/hr ,b = 7km/hr
rate of stream = ½ (28/3 – 7 )
= 7/6 = 1.1 km/hr

Time and Distance – Boats

1. If Nishu can swim downstream at 6kmph and upstream at 2kmph.What is his speed in still water ?
5 km/hr 4 km/hr 8 km/hr 7 km/hr

If the speed downloadstream is a km/ hr and the speed upstream is b km/ hr then Speed in still water is = ½ (a+b) km / hr [memory tool last 2 L cross and make +] Explanation: Given : speed downstream a = 6 km ph Speed upstream b = 2kmph Speed in still water = ½ (a+b) kmph = ½ (6+2) = 8/2 = 4kmph speed in still water = 4kmph

 2.Ashok can row upstream at 8kmph and downstream at 12kmph.What is the speed of the stream ?
6 km/hr 3 km/hr 2 km/hr 4 km/hr

Basic Formula: If the speed downstream is a kmph and the speed upstream is b kmph then Speed of the stream = ½ (a-b) kmph Explanation: Speed downstream a = 12kmph Speed upstream b = 8 kmph Speed of the stream = ½ (a-b) = ½ (12-8) = 4/2 = 2 kmph speed of the stream = 2kmph

 3.A man rows 750m in 775 seconds against the stream and returns in 7 1/2 minutes. What is rowing speed in still water ?
4.7km/hr 4 km/hr 3.5km/hr 6 km/hr

Basic Formula: i) Speed in still water = ½ (a+b) kmph where ‘a’ is speed downstream and ‘b’ is speed upstream ii) a km / hr = a x 5/18 m /s iii) a m/sec = a x 18/5 km/hr Explanation: Speed upstream ‘b’ = 750m / 775 sec = 30/31 m/sec Speed downstream ‘a’ = 750 m/ (15/2)minutes [ 1min=60 sec] a = 750m/450 sec =5/3 m/sec speed in still water = ½ (a+b) = ½ (750/450 + 750/675 ) m /sec = ½ (750/450 + 750/675 ) x 18/5 km/hr = ½ (5/3 + 30/31) x 18/5 km/hr = 4.7 km/hr

 4.A man can row 9 (1/3) kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. What is speed of the current ?
5km/hr 3(1/2) km/hr 4 (2/3) km/hr 8 (3/2)km/hr

Basic Formula: Speed of current = ½ (a-b) km/hr Explanation: Let man’s rate upstream be x km/hr. Then his rate downstream is 3 x km/hr Given: Speed in still water = 9 (1/3) = 28/3 km/hr i.e, ½ (a+b) = 28/3 km/hr ½ (x+3x) = 28/3 2x = 28/3 x = 28/ 2 x 3 = 14/3 km/hr rate upstream b = 14/3 km/hr and rate downstream a = 14/3 x 3 = 14 km/hr speed of the current = ½ (a-b) = ½ (14 – 14/3) = ½ (42-14/3) = 28/6 = 4 (2/3) km/hr

 5.Sham can row a boat at 10kmph in still water. IF the speed of the stream is 6kmph, the time taken to row a distance of 80km down the stream is
4 hours 5 hours 3 hours 2 hours

Basic Formula: Speed of stream = ½ (a-b) km/hr Speed in still water = ½ (a+b) km/hr Explanation: Given: Speed in still water, ½ (a+b) = 10 km/hr a+b = 20 km/hr…………….(1) speed of the stream, ½ (a-b) = 6km/hr a-b = 12 km/hr …………….(2) (1)+(2 ) we get 2a = 32 a = 16 km/hr speed downstream =distance traveled / time taken time taken = 80/16 = 5 hours