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

4.There is road besides a river. Two friends started from a place P, moved to a shopping mall
situated at another place Q and then returned to P again. One of them moves on a cycle at
a speed of 12 km/hr, while the other sails on a boat at a speed of 10 km/hr. If the river
flows at the speed of 4 km/hr, which of the two friends will return to place P?A. Both
B. Boater
C. Cyclist
D. None of these

Answer

Answer-C
Explanation:
The cyclist moves both ways at a speed of 12khr so average speed fo the
cyclist – 12 km/hr
boat sailor moves downstream at 10+4 = 14km/hr and upstream 10-
4 = 6km/hr
Average speed of the boat sailor = 2 x 14 x 6 / 14 +6 = 42/ 5 = 8.4km/hr
The average speed of cyclist is greater .so,cyclist comes first and return to
place P.

5.A this usual rowing rate, Mohit 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 miles 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.2.5m/hr
B.4 m/hr
C.8/3 m/hr
D. 5/3m/hr

Answer

Answer-C
Basic Formula:
Speed of the stream = ½ (a-b) km/hr
Explanation:
Let the speed in still water be x m/hr
Speed of stream be y m/hr
Then, speed upstream = x-y m/hr and
Speed downstream = x+y m/hr
12/x-y – 12 / x+y = 6 so,6 (x^2 – y^2) = 24 y
x^2 – y^2 = 4y
x^2 = y^2 + 4y…………..1
also
12/ 2x-y – 12/2x +y = 1 4x^2 – y^2 = 24y
x^2 = [24y + y^2] / 4 ……………….2
16y + 4y^2 = 24y + y2 [put X^2 value from 1] 3y^2 = 8 y so, y = 8/3
speed of the current = 8/3 m/hr = 2 (2/3) m/hr