A motorboat covers a distance of 16km upstream and 24km downstream
in 6 hours. In the same time it covers a distance of 12 km upstream and
36km downstream. Find the speed of the boat in still water and that of the
stream.
Answers
Answer:
Your answer is given below:-
Step-by-step explanation:
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:
Please find the attachment.
