Question

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.






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Answer 1

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,

$\tt \dfrac{16}{(x-y)} +\dfrac{24}{x+y} =6----(1)$

Now by the second case given,

$\tt \dfrac{12}{(x-y)} +\dfrac{36}{x+y} =6---(2)$

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.