Let the speed of the boat in still water be 'x' km/hr and speed of the stream be 'y' km/
Speed = Distance / Time
{tex}\therefore{/tex} {tex}\frac { 30 } { x - y } + \frac { 28 } { x + y } = 7{/tex}
and {tex}\frac { 21 } { x - y } + \frac { 21 } { x + y } = 5{/tex}
Let {tex}\frac { 1 } { x - y } \text { be } a \text { and } \frac { 1 } { x + y } \text { be } b{/tex}
30a + 28b = 7 ......(i)
21a + 21b = 5 ......(ii)
Multiplying (i) by 3 and (ii) by 4 and then subtracting.
{tex}90a+84b=21{/tex} ..............(iii)
{tex}84a+84b=20 {/tex} ..............(iv)
By solving (iii) and (iv)
{tex}90a-21=84a-20{/tex}
{tex}\Rightarrow{/tex}6a= 1
{tex}\Rightarrow{/tex} {tex}a = \frac { 1 } { 6 }{/tex}
Putting this value of ,a in eqn., (i),
{tex}30 \times \frac { 1 } { 6 } + 28 b = 7{/tex}
{tex}28 b = 7 - 30 \times \frac { 1 } { 6 } = 2{/tex}
{tex}\therefore{/tex}{tex}b = \frac { 1 } { 14 }{/tex}
x + y = 14 ...(iv)
Now, {tex}a = \frac { 1 } { x - y } = \frac { 1 } { 6 }{/tex}
{tex}\Rightarrow{/tex} x - y = 6
{tex}\Rightarrow{/tex}x = y + 6 .....(v)
Putting (iv) in (v)
y + 6 + y = 14
{tex}\Rightarrow{/tex} y = 4
Hence, speed of the boat in still water = 10 km/hr and speed of the stream = 4 km/hr.
Sia ? 4 years, 9 months ago
Let the speed of the boat in still water be 'x' km/hr and speed of the stream be 'y' km/
Speed = Distance / Time
{tex}\therefore{/tex} {tex}\frac { 30 } { x - y } + \frac { 28 } { x + y } = 7{/tex}
and {tex}\frac { 21 } { x - y } + \frac { 21 } { x + y } = 5{/tex}
Let {tex}\frac { 1 } { x - y } \text { be } a \text { and } \frac { 1 } { x + y } \text { be } b{/tex}
30a + 28b = 7 ......(i)
21a + 21b = 5 ......(ii)
Multiplying (i) by 3 and (ii) by 4 and then subtracting.
{tex}90a+84b=21{/tex} ..............(iii)
{tex}84a+84b=20 {/tex} ..............(iv)
By solving (iii) and (iv)
{tex}90a-21=84a-20{/tex}
{tex}\Rightarrow{/tex}6a= 1
{tex}\Rightarrow{/tex} {tex}a = \frac { 1 } { 6 }{/tex}
Putting this value of ,a in eqn., (i),
{tex}30 \times \frac { 1 } { 6 } + 28 b = 7{/tex}
{tex}28 b = 7 - 30 \times \frac { 1 } { 6 } = 2{/tex}
{tex}\therefore{/tex}{tex}b = \frac { 1 } { 14 }{/tex}
x + y = 14 ...(iv)
Now, {tex}a = \frac { 1 } { x - y } = \frac { 1 } { 6 }{/tex}
{tex}\Rightarrow{/tex} x - y = 6
{tex}\Rightarrow{/tex}x = y + 6 .....(v)
Putting (iv) in (v)
y + 6 + y = 14
{tex}\Rightarrow{/tex} y = 4
Hence, speed of the boat in still water = 10 km/hr and speed of the stream = 4 km/hr.
0Thank You