A boat goes 16 km upstream and 24 km downstream in 6 hrs. Also it covers 12 km upstream and 36 km downstream in the same time. Find the speed of the boat upstream and downstream.
Answers
Speed Upstream is y km per hour.
16/y+24/x =6••••••••••••••••{1}
12/y+ 36/x = 6•••••••••••••••{2}
x=2y
Putting values, x+y=6
3y=6
y=2
Speed Upstream = 2km per hour.
Speed Downstream =4 km per hour
Answer:
Speed of the stream = 4 km/hr
Speed of motorboat in still water = 8 km/hr
Step-by-step explanation:
Given:
Motorboat covers a distance of 16 km upstream and 24 km downstream in 6 hours.
It covers a distance of 12 km upstream and 36 km downstream again in 6 hours.
To Find:
Speed of the boat in still water.
Speed of the stream.
Solution:
Let the speed of the motorboat be x km/hr
Let speed of stream be y km/hr
We know that,
Speed while travelling upstream = (x - y) km/hr
Speed while travelling downstream = (x + y) km/hr
Also we know that,
Time = Distance/Speed
By the first case given,
16/(x-y) +24/(x+y) =6−−−−(1)
Now by the second case , given
12/(x-y) +36/(x+y) =6−−−(2)
Let us assume that 1/(x + y) = p, 1/(x - y) = q
Therefore equation 1 changes to,
16q + 24p = 6------(3)
12q + 36p = 6------(4)
Multiply equation 3 by 3 and equation 4 by 4
48q + 72p = 18---(5)
48q + 144p = 24---(6)
Solving equation 5 and 6 by elimination method,
72p = 6
p = 1/12
Now substitute the value of p in equation 5,
48q + 72 × 1/12 = 18
48q + 6 = 18
48q = 12
q = 1/4
Now we know that,
1/(x + y) = p
1/(x + y) = 1/12
x + y = 12
x = 12 - y ----(7)
Also,
1/(x - y) = 1/4
x - y = 4
Substitute value of x in the above equation,
12 -y - y = 4
12 - 2y = 4
2y = 8
y = 4
Hence the speed of the stream is 4 km/hr.
Substitute value of in equation 1,
x = 12 - 4
x = 8 km/hr
Hence the speed of the motorboat in still water is 8 km/hr.