Question

A person moves a certain distance in a certain time. If 1/3rd of the distance is
covered in 2/3rd of the time with speed u1 and rest of the 2/3rd in 1/3rd of the time with speed u2 then calculate u1/u2 = ?

Please answer very urgent

Answer 1

Given:

• A person moves a certain distance in a certain time.
• If 1/3rd of the distance is covered in 2/3rd of the time with speed u₁ and rest of the 2/3rd in 1/3rd of the time with speed u₂.

To calculate:

• u₁/u₂

Solution:

Let the total time taken be t.

• T₁ = 2t/3
• T₂ = t/3

Let the total distance travelled be x.

• D₁ = x/3
• D₂ = 2x/3

Let S be the speed,

• S₁ = u₁
• S₂ = u₂

We know that

♦ Speed = Distance/Time

According to question,

In first case

• u₁ = D₁/T₁
• u₁ = x/3/2t/3
• u₁ = x/3 × 3/2t
• u₁ = 3x/6t

In second case,

• u₂ = D₂/T₂
• u₂ = 2x/3/t/3
• u₂ = 2x/3 × 3/t
• u₂ = 6x/3t

Finally,

• u₁/u₂ = 3x/6t/6x/3t
• u₁/u₂ = 3x/6t × 3t/6x
• u₁/u₂ = 3x/6t × 3t/6x
• u₁/u₂ = 1/2 × 1/2
• u₁/u₂ = 1/4

Therefore,

★ u₁/u₂ = 1/4

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