Question

place A and B be are 30km apart and they are on a straight road. Hamid travels by A to B on bike. At the same time Joseph starts from B on bike, travels towards A. They meet each other after 20minuts. If Joseph would have started from B at that time but in the opposite direction C instead of towards A). Hamid would have caught him after 3hours. Find the speed of Hamid and Joseph ​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Distance between place A & B = 30 km

$\:\:$

• If Hamid travels by A to B on bike same time Joseph starts from B on bike, travels towards A, they meet each other after 20 minutes

$\:\:$

• If Joseph would have started from B at that time but in the opposite direction C instead of towards A then Hamid would have caught him after 3 hours

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Speed of Hamid and Joseph

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

• Let the speed of Joseph be "x"

• Let the speed of Hamid be "y"

$\:\:$

When Hamid travels by A to B on bike same time Joseph starts from B on bike then their combined velocity

$\:\:$

➠ x + y

$\:\:$

When Joseph would have started from B at that time but in the opposite direction C instead of towards A then their combined velocity

$\:\:$

➠ x - y

$\:\:$

$\underline{\bold{\texttt{We know that :}}}$

$\:\:$

➠ $\sf Time = \dfrac { Distance } { Speed }$ ------- (1)

$\:\:$

$\underline{\bold{\texttt{When they both travel in same direction :}}}$

$\:\:$

• Distance = 30 km

• Speed = x + y

• Time = 20 minutes

$\:\:$

Putting these values in (1)

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➠ $\sf \dfrac { 20 } { 60 } = \dfrac { 30} { x + y}$

$\:\:$

➜ $\sf \dfrac { 1 } { 3 } = \dfrac { 30} { x + y}$

$\:\:$

➜ $\sf \dfrac { 1 } { 3 } \times (x + y) = 30$

$\:\:$

➜ $\sf x + y = 30 \times 3$

$\:\:$

➜ x + y = 90 ------ (2)

$\:\:$

$\underline{\bold{\texttt{When they both travel in opposite direction :}}}$

$\:\:$

• Distance = 30 km

• Speed = x - y

• Time = 3 hours

$\:\:$

Putting these values in (1)

$\:\:$

➠ $\sf 3 = \dfrac { 30} { x - y}$

$\:\:$

➜ 3(x - y) = 30

$\:\:$

➜ x - y = 10 ------- (3)

$\:\:$

Adding equation (2) & (3)

$\:\:$

➜ x + y + x - y = 90 + 10

$\:\:$

➜ 2x = 100

$\:\:$

➜ $\sf x = \dfrac { 100 } { 2 }$

$\:\:$

➨ x = 50

$\:\:$

• Hence, Joseph is travelling with a speed of 50 km/hr

$\:\:$

Putting x = 50 in (2)

$\:\:$

➠ x + y = 90

$\:\:$

➜ 50 + y = 90

$\:\:$

➜ y = 90 - 50

$\:\:$

➨ y = 40

$\:\:$

• Hence, Hamid is travelling with a speed of 40 km/hr

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∴ Joseph and Hamid are travelling with speed 50 & 40 km/hr respectively

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Distance between place A & B = 30 km

$\:\:$

• If Hamid travels by A to B on bike same time Joseph starts from B on bike, travels towards A, they meet each other after 20 minutes

$\:\:$

• If Joseph would have started from B at that time but in the opposite direction C instead of towards A then Hamid would have caught him after 3 hours

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Speed of Hamid and Joseph

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the speed of Joseph be "x"

Let the speed of Hamid be "y"

$\:\:$

When Hamid travels by A to B on bike same time Joseph starts from B on bike then their combined velocity

$\:\:$

➠ x + y

$\:\:$

When Joseph would have started from B at that time but in the opposite direction C instead of towards A then their combined velocity

$\:\:$

➠ x - y

$\:\:$

$\underline{\bold{\texttt{We know that :}}}$

$\:\:$

➠ $\sf Time = \dfrac { Distance } { Speed }$ ------- (1)

$\:\:$

$\underline{\bold{\texttt{When they both travel in same direction :}}}$

$\:\:$

Distance = 30 km

Speed = x + y

Time = 20 minutes

$\:\:$

Putting these values in (1)

$\:\:$

➠ $\sf \dfrac { 20 } { 60 } = \dfrac { 30} { x + y}$

$\:\:$

➜ $\sf \dfrac { 1 } { 3 } = \dfrac { 30} { x + y}$

$\:\:$

➜ $\sf \dfrac { 1 } { 3 } \times (x + y) = 30$

$\:\:$

➜ $\sf x + y = 30 \times 3$

$\:\:$

➜ x + y = 90 ------ (2)

$\:\:$

$\underline{\bold{\texttt{When they both travel in opposite direction :}}}$

$\:\:$

Distance = 30 km

Speed = x - y

Time = 3 hours

$\:\:$

Putting these values in (1)

$\:\:$

➠ $\sf 3 = \dfrac { 30} { x - y}$

$\:\:$

➜ 3(x - y) = 30

$\:\:$

➜ x - y = 10 ------- (3)

$\:\:$

Adding equation (2) & (3)

$\:\:$

➜ x + y + x - y = 90 + 10

$\:\:$

➜ 2x = 100

$\:\:$

➜ $\sf x = \dfrac { 100 } { 2 }$

$\:\:$

➨ x = 50

$\:\:$

Hence, Joseph is travelling with a speed of 50 km/hr

$\:\:$

Putting x = 50 in (2)

$\:\:$

➠ x + y = 90

$\:\:$

➜ 50 + y = 90

$\:\:$

➜ y = 90 - 50

$\:\:$

➨ y = 40

$\:\:$

• Hence, Hamid is travelling with a speed of 40 km/hr

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• ∴ Joseph and Hamid are travelling with speed 50 & 40 km/hr respectively