Question

. A takes 3 hours more than B to walk 30 km. But if A doubles his pace, he is ahead of B

by one and half hrs. Find their speed of walking.​

Answer 1

GivEn:

• Distance = 30 km

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To find:

• Speed of walking.

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SoluTion:

☯ Let speed of A be x km/h

☯ Let speed of B be y km/h

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We know that,

$\star\;{\boxed{\bf{Speed = \dfrac{Distance}{Time}}}}$

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Therefore,

☯ Time taken by A to cover 30 km = $\sf \dfrac{30}{x}$

☯ Time taken by B to cover 30 km = $\sf \dfrac{30}{y}$

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$\boxed{\bf{\mid{\overline{\underline{\bigstar\: According\: to\: Question :}}}}\mid}$

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◉ A takes 3 hours more than B to walk 30 km.

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$:\implies\sf \dfrac{30}{x} = \dfrac{30}{y} + 3$

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$:\implies\sf \dfrac{30}{x} - \dfrac{30}{y} = 3\;\;\;\;\;\bigg[eq\;(1)\bigg]$

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Also,

◉ When A doubles his pace, he is ahead of B by one and half hrs.

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So,

When A doubles his speed, then the time taken by A = $\sf \dfrac{30}{2x}$.

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Therefore,

$:\implies\sf \dfrac{30}{y} = \dfrac{30}{2x} + \dfrac{3}{2}$

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$:\implies\sf \dfrac{30}{y} - \dfrac{ \cancel{30}}{ \cancel{2}x} = \dfrac{3}{2}$

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$:\implies\sf \dfrac{30}{y} - \dfrac{15}{x} = \dfrac{3}{2}\;\;\;\;\;\bigg[eq\;(1)\bigg]$

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Now, Let's assume $\sf \dfrac{1}{x}$ as p and $\sf \dfrac{1}{y}$ as q,

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★ Put these value in eq (1) and eq (2),

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$:\implies\sf 30p - 30q = 3\;\;\;\;\;\bigg[eq\;(3)\bigg]$

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$:\implies\sf 30q - 15p = \dfrac{3}{2}\;\;\;\;\;\bigg[eq\;(4)\bigg]$

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★ Adding eq(3) and eq(4), we get,

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$:\implies\sf 15p = \dfrac{9}{2}$

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$:\implies\sf p = \dfrac{9}{2 \times 15}$

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$:\implies\bf p = \dfrac{3}{10}$

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★ Substituting value of p in eq(3),

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$:\implies\sf 30p - 30q = 3$

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$:\implies\sf \cancel{30} \times \dfrac{3}{ \cancel{10}} - 30q = 3$

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$:\implies\sf 3 \times 3 - 30q = 3$

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$:\implies\sf 9 - 30q = 3$

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$:\implies\sf - 30q = 3 - 9$

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$:\implies\sf - 30q = - 6$

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$:\implies\sf q = \cancel{ \dfrac{-30}{-6}}$

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$:\implies\bf q = \dfrac{1}{5}$

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Therefore,

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We know that,

$\dashrightarrow\sf \dfrac{1}{y} = q$

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$\dashrightarrow\sf \dfrac{1}{y} = \dfrac{1}{5}$

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$\dashrightarrow{\underline{\boxed{\sf{y = 5\;km/h}}}}\;\bigstar$

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And,

$\dashrightarrow\sf \dfrac{1}{x} = p$

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$\dashrightarrow\sf \dfrac{1}{x} = \dfrac{3}{10}$

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$\dashrightarrow{\underline{\boxed{\sf{y = \dfrac{10}{3}\;km/h}}}}\;\bigstar$

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$\therefore$ Hence, Speed of A and B is $\bf \dfrac{10}{3}$ km/h and 5 km/h respectively.