BE
i GH
On Monday, a boat goes 6 km upstream and 24 km downstream in 7
hours But on Tuesday, the same boat takes 4 hours more than on
Monday to go 10 km upstream and 36 km downstream. Determine
the speed of the boat in still water and the speed of the stream.
US
LETS
Answers
Let speed of the boat in still water =xkm/hr and speed of the stream =ykm/hr
Then, the speed of the boat downstream =(x+y)km/hr And speed of the boat upstream =(x−y)km/hr
According to the question
Condition I:
When boat goes 16km upstream, let the time taken be
t
1
. Then,
t
1
=
x−y
16
h[∵time=
speed
distance
]
When boat goes 24km downstream, let the time taken be t
2
.
Then, t
2
=
x+y
24
h
But total time taken (t
1
+t
2
)=6 hours
∴
x−y
16
+
x+y
24
=6…(a)
Condition II:
When boat goes 12km upstream, let the time taken be T
1
Then, T
1
=
x−y
12
h[∵ time =
speed
distance
]
When boat goes 36km downstream, let the time taken be T
2
. Then,
T
2
=
x+y
36
h
But total time taken (T
1
+T
2
)=6 hours
∴
x−y
12
+
x+y
36
=6…(b)
Now, we solve tis pair of linear equations by elimination method
x+y
16
+
x−y
24
=6…(i)
And
x+y
12
+
x−y
36
=6…(ii)
On multiplying Eq. (i) by 3 and Eq. (ii) by 4 to make the coefficients equal of first term, we get the equation as
x+y
48
+
x−y
72
=18…(iii)
x+y
48
+
x−y
144
=24…(iv)
On substracting Eq. (iii) from Eq. (iv), we get
⇒
x+y
16
+
12
24
=6
⇒
x+y
16
=6−2
⇒
x+y
16
=4
⇒x+y=4…(b)
Adding Eq. (a) and (b), we get ⇒2x=16
⇒x=8
On putting value of x=8 in eq. (a), we get 8−y=12
⇒y=−4 but speed can't be negative ⇒y=4
Hence, x=8 and y=4, which is the required solution.
Hence, the speed of the boat in still water is 8km/hr and speed of the stream is 4km/hr.