Question

A and B are two stations 560 km apart A train starts from A at 7 am and travels towards B at 80 km/ hr. Another train starts from B at 9 am and travels towards A at 120 km/h . When will they meet eachother?​

Answer 1

Given :

• The distance between station A and station B is 560 km .
• A train starts from Station A towards station B at a speed of 80 km/h .
• Anather train starts from Station B towards station A at a speed of 120 km/h .

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To Find :

• When they will meet eachother = ?

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Solution :

~ Formula Used :

• Distance :

${\color{cyan}{\bigstar}} \; \; {\underline{\boxed{\red{\sf{ Distance = Speed \times Time }}}}}$

• Time :

${\color{cyan}{\bigstar}} \; \; {\underline{\boxed{\red{\sf{ Time = \dfrac{Distance}{Speed} }}}}}$

Let :

• ➳ ${\sf{T_1}}$ = Train started from Station A
• ➳ ${\sf{T_2}}$ = Train started from Station B

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${\large{\color{darkblue}{\pmb{\frak{ \; Note \; :- }}}}}$

➳ As ${\sf{T_1}}$ starts at 7 AM and ${\sf{T_2}}$ starts at 9 AM .There is a time gap of 2 hrs . So, we will first calculate the distance covered by ${\sf{T_1}}$ in this interval of time .Let's Find :

~ Calculating the Distance Covered by ${\sf{T_1}}$ in 2 hrs :

$\; \; \dashrightarrow \sf \; \; { D_1 = S_1 \times T_1 }$

$\; \; \dashrightarrow \sf \; \; { D_1 = 80 \times 2 }$

$\; \; {\color{green} {\dashrightarrow}}\; \; \; {\underline{\boxed{\red{\sf{D_1 = 160 \; km }}}}}$

~ Distance left to cover by ${\sf{T_1}}$ :

$\; \; \dashrightarrow \sf \; \; {Distance \; Left = Total \; Distance - D_1 }$

$\; \; \dashrightarrow \sf \; \; {Distance \; Left = 560 - 160 }$

$\; \; {\color{maroon} {\dashrightarrow}}\; \; \; {\underline{\boxed{\pink{\sf{ Distance \; Left = 400 \; km }}}}}$

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~ There two trains will meet :

$\; \; \longmapsto \sf \; \; { Trains{\small_{(Meet)}} = \dfrac{Distance \; Left }{Sum \; of \; Speed }}$

$\; \; \longmapsto \sf \; \; { Trains{\small_{(Meet)}} = \dfrac{400 }{80 + 120 }}$

$\; \; \longmapsto \sf \; \; { Trains{\small_{(Meet)}} = \dfrac{400 }{200 }}$

$\; \; \longmapsto \sf \; \; { Trains{\small_{(Meet)}} = \cancel\dfrac{400 }{200 }}$

$\; \; {\color{orange} {\dashrightarrow}}\; \; \; {\underline{\boxed{\color{darkblue}{\sf{ They'll \; meet \; in = 2 \: hrs }}}}}$

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~ Time at which they'll meet :

$\; \; \longmapsto \sf \; \; { Time{\small_{(They'll \; Meet )}} = Starting \; Time{\small_{(T_2)}} + Time }$

$\; \; \longmapsto \sf \; \; { Time{\small_{(They'll \; Meet )}} = 9 \: AM + 2 \: hrs }$

$\; \; {\color{cyan} {\dashrightarrow}} \; \; \; {\underline{\boxed{\color{maroon}{\sf{ They'll \; meet \; at = 11 \: AM }}}}}$

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~ Therefore :

❝ These two trains will meet at 11 AM . ❞

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