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

Boats and Streams

1. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
A. 8.5 km/hr	B. 10 km/hr.
C. 12.5 km/hr	D. 9 km/hr

Answer : Option B

Explanation :

Man's speed with the current = 15 km/hr

=>speed of the man + speed of the current = 15 km/hr

speed of the current is 2.5 km/hr

Hence, speed of the man = 15 - 2.5 = 12.5 km/hr

man's speed against the current = speed of the man - speed of the current

= 12.5 - 2.5 = 10 km/hr

2. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
A. 10	B. 6
C. 5	D. 4

Answer : Option C

Time taken downstream = 30(15+v)

Time taken upstream = 30(15−v)

total time = 30(15+v)+30(15−v)

It is given that total time is 4 hours 30 minutes = 412 hour 
                                                                 = 92 houri.e., 30(15+v)+30(15−v)=92
⇒1(15+v)+1(15−v)=92×30=320

⇒15−v+15+v(15+v)(15−v)=320

⇒30152−v2=320⇒30225−v2=320

⇒10225−v2=120⇒225−v2=200

⇒v2=225−200=25

⇒v=5 km/hr