Question

pls answer it fast pls....​

Answer 1

$\sf\huge{\underline{Question :}}$

Two runners A and B cover the same distance at the rate of 20 km/h and 21 km/h, respectively. If runner A takes 1.5 minutes more, then total distance travelled by both is equal to

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$\sf\huge{\underline{Answer :}}$

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Previous Knowledge Req. :—»

$\sf \: Distance \: Covered \: = Average \: Speed \: \times \: Time \: Elapsed$

1 km = 1000 m

1 hr = 60 mins = 3600 secs

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Given :—»

Two runners A and B Running with Speed 20km/h and 21km/h respectively. Difference btw time taken by both i.e 1.5 mins.

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To Find :—»

Distance they travelled

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Solution :—»

20 km/h = $20 \times \dfrac{1000}{3600}$

$\longrightarrow \dfrac{50}{9}$m/s

20 km/h = $21 \times \dfrac{1000}{3600}$

$\longrightarrow \dfrac{105}{18}$m/s

1.5mins = $1.5 \times 60$

$\longrightarrow 90 Secs$

Let the Distance Travelled be D

So, ATQ

$\dfrac{D \times 18}{105} = \: t$⠀⠀ ——Eq. of runner B

$\dfrac{D \times 9}{50} = t + 90 \: secs$ ⠀⠀—— Eq. of runner A

$\dfrac{D \times 9}{50} = \dfrac{D \times 18}{105} + 90$⠀⠀ —— Using both Eq

$\dfrac{D \times \cancel{9}\: \: ^{1} }{50} = \dfrac{D \times \cancel{18}\: \: ^{2} }{105} + \cancel{90} \: \: ^{10}$

$\dfrac{D }{50} - \dfrac{2D}{105} = 10$

$\dfrac{D(21 - 20)}{1050} = \: 10$

$D \: = \: 10500 \: \: Metres$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

D = 10.5 km