Question

In a kilometer race, if a gives b a 40 m start, a wins by 19 sec but if a gives b a 30 s start, b wins by 40 m. Find the time taken by b to run 5,000 m?

Answer 1

Answer: 12.5 hr.

Step-by-step explanation:Analyzing the 2 cases,Case1: when A travels 1Km,B travels 960 – 19 x where B’s speed=x m/s Case 2:when A travels 960 m,B travels 1000-30 x In both cases,time remains constant.therefor,Distance is directly proportional to speed. 1000/(960-19x) = 960/(1000-30x) solving x,we get x=20/3 m/s.Time taken to travel 5000 m for B is 12.5 hr.

Answer 2

Therefore the time taken by 'B' to run 5000 m is '750 seconds'.

Given:

'A' wins by 19 seconds in a kilometer race if 'A' gives 'B' a 40 m start.

'B' wins by 40 m in a kilometer race if 'A' gives 'B' a 30 seconds start.

To Find:

The time taken by 'B' to run 5000 m.

Solution:

The given question can be solved very easily as shown below.

Let Time taken by 'A' = T₁

Let Time taken by 'B' = T₂

Let Velocity of 'A' = V₁

Let Velocity of 'B' = V₂

⇒ Velocity = Distance / Time

Case-1:

'A' wins by 19 seconds in a kilometer race if 'A' gives 'B' a 40 m start.

In this case,

Distance travelled by 'A' = 1000 m

Distance travelled by 'B' = 1000 - 40 = 960 m

Time taken by 'A' = Time taken by 'B' - 19 ⇒ T₁ = T₂ - 19_______(i.)

Substitute the values in the velocity equation 'A' and 'B',

Velocity of 'A' = V₁ = 1000 / T₁ ⇒ T₁ = 1000 / V₁

Velocity of 'B' = V₂ = 960 / T₂ ⇒ T₂ = 960 / V₂

Substitute T₁ and T₂ values in equation-(i.),

⇒ T₁ = T₂ - 19

⇒ 1000 / V₁ = 960 / V₂ - 19______(ii.)

Case-2:

'B' wins by 40 m in a kilometer race if 'A' gives 'B' a 30 seconds start.

In this case,

Distance travelled by 'A' = 1000 - 40 = 960 m

Distance travelled by 'B' = 1000

Time taken by 'A' = Time taken by 'B' - 30 ⇒ T₁ = T₂ - 30_____(iii.)

Substitute the values in the velocity equation of 'A' and 'B',

Velocity of 'A' = V₁ = 960 / T₁ ⇒ T₁ = 960 / V₁

Velocity of 'B' = V₂ = 1000 / T₂ ⇒ T₂ = 1000 / V₂

Substitute T₁ and T₂ values in equation-(iii.),

⇒ T₁ = T₂ - 30

⇒ 960 / V₁ = 1000 / V₂ - 30______(iv.)

Dividing eq-(ii.) by eq-(iv.),

⇒ ( 1000 / V₁ ) / ( 960 / V₁ ) = ( 960 / V₂ - 19 ) / ( 1000 / V₂ - 30 )

⇒ 1000 / 960 = ( 960 - 19V₂ ) / ( 1000 - 30V₂ )

⇒ 25 / 24 = ( 960 - 19V₂ ) / ( 1000 - 30V₂ )

⇒ 25 ( 1000 - 30V₂ ) = 24 ( 960 - 19V₂ )

⇒ 25,000 - 750V₂ = 23,040 - 456V₂

⇒ 25,000 - 23,040 = V₂( 750 - 456 )

⇒ 1,960 = 294V₂

⇒ V₂ = 6.67 m/s

Now Time taken by 'B' to run 5,000 m is given by,

T = 5000 / V₂ = 5000 / 6.67 ≅ 750 sec

Therefore the time taken by 'B' to run 5000 m is '750 seconds'.

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