Question

A train covered a certain distance as a uniform speed. if The Speed of thE train would have been 15 km/h more, it would have taKe 1.2h Less than the schedule time. If the speed of the train would have been 12 km/h less, it works have taken 1.5 h more than the schedule time. Find the distance covered by threatening.

Answer 1

$\huge\bf{\red{\underline{\underline{Solution:-}}}}$

Let the uniform speed of the train be x km/hr.

and the actual time taken to cover certain distance be y hours.

$\bf{\red{\boxed{\boxed{\blue{Formula}}}}}$

$\bf{Distance = speed\times {time}}$

⠀⠀⠀⠀⠀⠀⛬ The distance covered by threatening train is xy km.

From the 1st condition,

Speed of the train is (x + 15) km/hr and the time to cover the distance = ( y - 1.2) hours .

⛬ (x + 15)(y + 1.2) = xy

⛬ xy + 15y - 1.2x - 18 = xy

⛬ 15y - 1.2x = 18 ...............(1)

Similarly, from the second condition,

speed of the train is ( x - 12) km/hr and the time taken to cover the distance = ( y + 1.5) hours .

(x - 12)(y + 1.5) = xy

⛬ xy - 12y + 1.5x - 18 = xy

⛬ - 12y + 1.5x = 18 .........(2)

Now ,

15y - 1.2x = 18 ........................(1)

- 12y + 1.5x = 18 ...........................(2)

Multiplying equation (1) by 4

and equation (2) by 5

we get,

60y - 4.8x = 72 .....................(3)

- 60y + 7.5x = 90 ...........................(4)

Let's add the equation (3) and (4)

60y - 4.8x = 72 ..................(3)

- 60y + 7.5x = 90 ..................(4)

◃───────────▹

⠀⠀⠀ ⠀2.7x = 162

$\bf\frac{162}{2.7}$

$\bf\frac{162 \times10}{27}\bf{= 6 \times {10}}$

⛬ x = 60

now substituting

put x = 60 in equation (1),

15y - 1.2x = 18 ..................(1)

$\bf{15y - 1.2\times{60} = 18}$

⛬ 15y - 72 = 18

⛬ 15y = 18 + 72

⛬ 15y = 90

⛬ $\bf\frac{90}{15}$

⛬ y = 6

Now, Finding the distance covered by the train.

so,

xy = 60 * 6 = 360 km.

Ans. The distance covered by the train is 360 km.

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Answer 2

Answer:

Let the uniform speed of the train be x km/hr.

and the actual time taken to cover certain distance be y hours.

\bf{\red{\boxed{\boxed{\blue{Formula}}}}}

Formula

\bf{Distance = speed\times {time}}Distance=speed×time

⠀⠀⠀⠀⠀⠀⛬ The distance covered by threatening train is xy km.

From the 1st condition,

Speed of the train is (x + 15) km/hr and the time to cover the distance = ( y - 1.2) hours .

⛬ (x + 15)(y + 1.2) = xy

⛬ xy + 15y - 1.2x - 18 = xy

⛬ 15y - 1.2x = 18 ...............(1)

Similarly, from the second condition,

speed of the train is ( x - 12) km/hr and the time taken to cover the distance = ( y + 1.5) hours .

(x - 12)(y + 1.5) = xy

⛬ xy - 12y + 1.5x - 18 = xy

⛬ - 12y + 1.5x = 18 .........(2)

Now ,

15y - 1.2x = 18 ........................(1)

- 12y + 1.5x = 18 ...........................(2)

Multiplying equation (1) by 4

and equation (2) by 5

we get,

60y - 4.8x = 72 .....................(3)

- 60y + 7.5x = 90 ...........................(4)

Let's add the equation (3) and (4)

60y - 4.8x = 72 ..................(3)

- 60y + 7.5x = 90 ..................(4)

◃───────────▹

⠀⠀⠀ ⠀2.7x = 162

\bf\frac{162}{2.7}

2.7

162

\bf\frac{162 \times10}{27}\bf{= 6 \times {10}}

27

162×10

=6×10

⛬ x = 60

now substituting

put x = 60 in equation (1),

15y - 1.2x = 18 ..................(1)

\bf{15y - 1.2\times{60} = 18}15y−1.2×60=18

⛬ 15y - 72 = 18

⛬ 15y = 18 + 72

⛬ 15y = 90

⛬ \bf\frac{90}{15}

15

90

⛬ y = 6

Now, Finding the distance covered by the train.

so,

xy = 60 * 6 = 360 km.