A boat goes 16 km upstream and 24 km downstream in 6 hours. Also, it covers 12 km upstream and 36 km downstream in the same time. Find the speed of the boat in still water and that of the stream.
Answers
Answer:
Let speed of the boat in still water =x km/hr, and
Speed of the current =y km/hr
Downstream speed =(x+y) km/hr
Upstream speed =(x−y) km/hr
T=
S
D
x+y
24
+
x−y
16
=6 .......(1)
x+y
36
+
x−y
12
=6 .......(2)
Put
x+y
1
=u and
x−y
1
=v the above equation becomes,
24u+16v=6
Or, 12u+8v=3 ... (3)
36u+12v=6
Or, 6u+2v=1 ... (4)
Multiplying (4) by 4, we get,
24u+8v=4v … (5)
Subtracting (3) by (5), we get,
12u=1
⇒u=
12
1
Putting the value of u in (4), we get, v=
4
1
⇒
x+y
1
=
12
1
and
x−y
1
=
4
1
⇒x+y=12 and x−y=4
Thus, speed of the boat upstream =4 km/hr
Speed of the boat downstream =12 km/hr
Step-by-step explanation:
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i had given the ans step by step
Step-by-step explanation:
Explanation:
Let the speed of the boat in still water be x km/hr.
Let the speed of the current be y km/hr.
The speed of the boat downstream = x + y
The speed of the boat upstream = x - y
Given that the boat goes 16km upstream and 24 km downstream in 6 hours.
= > (16/x - y) + (24/x + y) = 6 ------- (1)
Given that it covers 12km upstream and 36km downstream in same time.
= > (12/x - y) + (36/x + y) = 6 -------- (2)
On solving (1) * 3 & (2) * 4, we get
Let 1/x - y = u, 1/x + y = v
Now,
48u + 72v = 18
48u + 144v = 24
---------------------------
-72v = -6
v = 1/12
Substitute v = 12, we get
48u + 72v = 18
48u + 72(1/12) = 18
48u + 6 = 18
48u = 18 - 6
48u = 12
u = 12/48
u = 1/4.
Hence, u = 1/4
=> 1/x - y = (1/4)
=> x - y = 4.
Hence, v = 1/12.
=> 1/x + y = 1/12
=> x + y = 12.
Verification:
Let us take x = 8, y = 4.
=> 8 + 4 = 12
=> 8 - 4 = 4.
Therefore Speed of the boat in still water = 8 km/hr.