Boat & Stream
Question
Q1.
A person can row
1/10
km upstream in 12 minutes
and return in 8 minutes . Find the speed of man in still water .
Solution.
distance = speed x time
1/10
= speed x
12/60
(upstream)
=
1/2
km/h
1/10
= speed x
8/60
speed =
6/8
=
3/4
km/h
speed in still water =
=
5/8
km/h
Solution
Q2.
The speed of a boat in stil water is 10km/hr. It covers (upstream)a distance of 45km in 6 hrs. The speed(in km/hr) of the stream is.
(a)2.5 (b)3 (c)3.5 (d)4
Solution.
Upstream speed of boat
=Distance/Time = 45/6 = 15/2
= 7.5 km/hr
Speed of current = 10 - 7.5
= 2.5 kmph
Solution
Q3.
A can row a certain distance downstream in 6 hrs and return the same distance in 9 hrs . If the stream flows at the rate of 3 km/hr. find
the speed of A in still water.
(a) 20 km/hr (b) 15 km/hr (c) 10 km/hr (d) 5 km/hr
Solution.
m be the speed of boat in still water,z is the speed of stream.
s1 t1 = s2 t2
6(m + z) = 9(m -z)
6(m + 3) = 9(m - 3)
6m + 18 = 9m - 27
45 = 3m
m = 15
Solution
Q4.
A person can sail 15 km/hr in still water . He takes twice as long as to row up as to row down the river . find the rate of stream .
Solution.
Assume person's rate with current = x km/hr
and person's rate against the current =
x/2
as per question
person's rate in still water =
1/2
(x +
x/2
)
3x/4
= 15 → x = 20
rate of stream is =
1/2
(20 - 10) = 5 km/hr
or
let the rate of stream = x km/hr
15 + x = 2(15 - x)
15 + x = 30 - 2x ⇒
- 15 = - 3x ⇒ x = 5 km/hr
Solution
Q5.
A person swims downstream 40 km and upstream 32 km, taking 8 hrs each time. Find the velocity of current ?
(a) 0.9 km/hr
(b) 0.5 km/hr (c) 1 km/hr (d) 2 km/hr
Solution.
Person's rate downstream = 5 km/hr
Person's rate upstream = 4 km/hr
x = Person's rate in still water
y = rate of the current
x + y = 5
x - y = 4
2x = 9
x = 4.5 km/hr
y = 0.5 km/hr
Solution
Q6.
A man can row 15km/hr downstream and 9 km/hr upstream. The speed of the boat in still water is.
(a)8 km/hr (b)10 km/hr (c)15 km/hr (d)12 km/hr
Solution.
Speed of boat in still water
= 1/2(Rate downstream + Rate upstream)
= 1/2(15 + 9)
= 1/2 x 24 = 12 km/hr.
Solution
Q7.
A person can swim downstream at 20 km/hr and can swim upstream at 18 km/hr . Find the person's speed in still water and the rate
of the stream ?
Solution.
Rate of person in still water =
1/2
(person's speed in downstream + person's
speed in upstream)
=
1/2
(20 + 18) =
1/2
(38) =
19 km/hr .
Rate of stream (current) =
1/2
(person's speed in downstream - person's
speed in upstream)
=
1/2
(20 - 18) =
1/2
(2) =
1 km/hr .
Solution
Q8.
A motorboat covers 36 km in a hour in still water towards upstream it covers 56 km in 1 hr 45 min . find the time to cover
the same distance in the direction of river .
Solution.
speed of boat in still water is 36 km/h
upstream speed =
56/105
x 60 = 32 km/h
so,speed of river (flow) is 4 km/h
downstream speed is = 40 km/h
time to cover 56 km (downstream) =
56/40
1
16/40
=
1
2/5
= 1 hr 24 min .
Solution
Q9.
Samir can row a certain distance downstream in 6 hours and return the same distance in 12 hours . If the current rate is 2 km/hr . find
speed of samir in still water .
Solution.
Let the speed of samir in still water is A
6(2 + A) = 12(A - 2)
12 + 6A = 12A - 24
- 6A = - 36
A = 6 km/hr
Short cut
=
CR(TD + TU)/( TU - TD)
=
2(6 + 12)/(12 - 6)
=
36/6
C
r =
Current rate
T
D = Downstream time , T
U = Upstream time .
Solution
Q10.
A person can row a certain distance downstream in 9 hours and return in 12 hours . Speed of current is 3 km/hr , find the speed of person
in still water and one side distance .
Solution.
Let speed of person in still water is m km/hr.
9(m + 3) = 12(m - 3)
9m + 27 = 12m - 36
-3m = - 63
m = 21 km/hr
distance = 24 x 9 = 216 km
Short cut
=
Cr(TD + TU)/( TU - TD)
=
3(12 + 9)/12 - 9
=
3 x 21/3
= 21 km/hr
distance = 24 x 9 = 216 km
Solution
