Question

Two runners start from the same point at the same time. They
will be 4 miles apart at the end of two hours if running in the
same direction, and they will be 16 miles apart at the end of one
hour if running in opposite directions. Find their speeds

Answer 1

Given :-

• if Two Runners run in same direction they will be 4 miles Apart In 2 Hours..
• if Two Runners run in Opposite direction they will be 16 miles Apart In 1 Hours..

To Find :-

• Speed of Both Runners ?

Concept used :-

• in Same Direction Speed is Reduced. So, usual Speed is Difference of Both.
• in Opposite Direction Speed is Increased. So, usual Speed is Sum of Both.
• Distance = Speed * Time.

Solution :-

Let us Assume That, Speed of Both Runners is S₁ & S₂ , where S₁ > S₂...

So,

→ In same Direction usual Speed = S₁ - S₂

→ total Time = 2 Hours.

→ Total Distance covered = S * T = 2(S₁ - S₂)

Hence,

→ 2(S₁ - S₂) = 4 Miles

→ (S₁ - S₂) = 2 ------------ Equation ❶

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And,

→ In Opposite Direction usual Speed = S₁ + S₂

→ total Time = 1 Hours.

→ Total Distance covered = S * T = 1(S₁ + S₂)

Hence,

→ (S₁ + S₂) = 16 Miles ----------- Equation ❷

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Adding Both Equations we get :-

→ (S₁ - S₂) + (S₁ + S₂) = 2 + 16

→ 2S₁ = 18

→ S₁ = 9 Miles / Hour . (Ans.)

Putting This value in Equation ❶ Now,

→ 9 - S₂ = 2

→ S₂ = 9 - 2

→ S₂ = 7 Miles / Hour . (Ans.)

Hence, Speed of Both Runners are 9 Miles / Hour & 7 Miles / Hour..

Answer 2

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$\huge\tt{GIVEN:}$

• Two runners start from the same point at the same time.
• They will be 4 miles apart at the end of two hours if running in the same direction, and they will be 16 miles apart at the end of one hour if running in opposite directions.

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$\huge\tt{TO~FIND:}$

• Their speeds

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$\huge\tt{SOLUTION:}$

Let the Speed of Both Runners be S₁ & S₂ , where we know that S₁ > S₂

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Then,

➠ In same Direction, normal Speed = S₁ - S₂

➠ total Time = 2 Hours.

➠ Total Distance covered = S * T = 2(S₁ - S₂)

➠2(S₁ - S₂) = 4 Miles

➠(S₁ - S₂) = 2 _______(EQ.1)

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Now,

➠In Opposite Direction ,normal Speed = S₁ + S₂

➠ total Time = 1 Hours.

➠ Total Distance covered = S * T = 1(S₁ + S₂)

➠ (S₁ + S₂) = 16 Miles ______(EQ.2)

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As we have got our equations,

We'll compare them.....

➠ (S₁ - S₂) + (S₁ + S₂) = 2 + 16

➠2S₁ = 18

➠S₁ = 9 Miles / Hour

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➠9 - S₂ = 2

➠ S₂ = 9 - 2

➠S₂ = 7 Miles / Hour

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$\tt\red{Speed(1)~=~9~ Miles~ / Hour }$

$\tt\purple{Speed(2)~ =~ 7~ Miles ~/ Hour }$

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