Question

A train has to cover 360 km in 6 hours. It travels at a speed of 55 km per hour for
the first four hours. To reach the destination in the desired time, what should
be the
speed of the train to cover the remaining distance?​

Answer 1

Answer:

$\orange{\bold{\underbrace{\overbrace{❥Answer᎓}}}}$

Integrate the function

$\huge\green\tt\frac{ \sqrt{tanx} }{sinxcosx}}$

⇛$\huge\tt\frac{ \sqrt{tanx} }{sinxcosx}$

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⇛$\huge\tt \frac{ \sqrt{tanx} }{sinxcosx \times \frac{cosx}{cosx}}$

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⇛$\huge\tt \frac{ \sqrt{tanx} }{sinx \times \frac{ {cos}^{2} x}{cosx}}$ ㅤ ㅤ ㅤ

⇛ $\huge\tt\frac{ \sqrt{tanx} }{ {cos}^{2} x \times \frac{sinx}{cosx} }$

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⇛$\huge\tt\frac{ \sqrt{tanx} }{ {cos}^{2}x \times tanx }$

⇛$\huge\tt {tan}^{ \frac{1}{2} - 1 } \times \frac{1}{ {cos}^{2} x}$ㅤ ㅤ ㅤ ㅤ ㅤ

⇛$\huge\tt {(tan)}^{ - \frac{ 1}{2} } \times \frac{1}{ {cos}^{2}x } = {(tanx)}^{ - \frac{1}{2} } \times {sec}^{2} x⇛(tan)$

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⇛$\huge\tt {(tan)}^{ - \frac{ 1}{2} } \times \frac{1}{ {cos}^{2}x } = ∫ {(tanx)}^{ - \frac{1}{2} } \times {sec}^{2} x \times dx⇛(tan)$

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$\bold\blue{☛\: Let tanx=t}$

$\bold\blue{☛ \:Differentiating \: both \: sides \: w.r.t.x}$

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⇛$\huge\tt {sec}^{2} x = \frac{dt}{dx}$

⇛$\huge\tt{dx \frac{dt}{ {sec}^{2}x }}$

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⇛$\huge\tt∴∫ {(tanx)}^{ - \frac{1}{2} } \times {sec}^{2} x \times dx$

⇛$\huge\tt ∫ {(t)}^{ - \frac{1}{2} } \times {sec}^{2} x \times \frac{dt}{ {sec}^{2}x }$

⇛$\huge\tt ∫ {t}^{ - \frac{1}{2} }$ㅤ ㅤ

⇛ $\huge\tt\frac{ {t}^{ - \frac{1}{2} + 1} }{ - \frac{1}{2} + 1 }$

⇛ $\huge\tt \frac{ {t}^{ \frac{1}{2} } }{ \frac{1}{2} } + c = 2 {t}^{ \frac{1}{2} } + c = 2 \sqrt{t}$

⇛$\huge2 \sqrt{t} + c = 2 \sqrt{tanx}$

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Answer 2

★ Given and To Find :

A train has to cover 360 km in 6 hours. It travels at a speed of 55 km/h for  the first 4hours. To reach the destination in the desired time, what should  be the speed of the train to cover the remaining distance ?

★ Solution :

Total distance to be covered = 360 km

Total time = 6 h

Speed for 4 hours = 55 km/h

So , Distance for 4 hours is ,

➠$Speed=\frac{Distance}{Time}$

➠$55=\frac{D}{4}$

➠$D=220 km$★

Distance covered in first 4 hours is 220 km .

Remaining distance = Total distance - Distance covered in first 4 hours

➠ R.D = 360 - 220

➠ R.D = 140 km  ★

Remaining time = Total time - 4 hours

➠ R.T = 6 - 4

➠ R.T = 2 h  ★

So , Speed of the train for remaining distance is ,

$Speed_{R} =\frac{Remaining Distance}{RemainingTime}$

$Speed_R=\frac{R.D}{R.T}$

$Speed_R=\frac{140}{2}$

$Speed_R=70 km/h$ ★