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Course / Category - 10th NTSE

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NTSE

10th NTSE

BASIC

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NTSE

10th NTSE

Self Learning

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Maths / Polynomials / Problems Based on Speed

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Solving Statements Involving Speed

Solving Statements Involving Speed:

In these types of problems we consider the relative speed of the two objects. When the two objects are moving in the same direction, the relative speed is the difference of the speed of the two objects. When the two objects are moving in the opposite direction , the relative speed is found as the sum of speed of the two objects.

Illustration: A train travels a distance of 300 km at a certain constant speed. If the speed of train is increased by 5 km an hour it takes two hours less . Find the original speed of train.

Solution: Let the speed of train = x km/h

distance= 300km

$Speed = frac{distance}{time}$

$time = frac{distance}{speed}$

$time_{original} = frac{300}{x}$

New Speed= x+5

$time_{new} = frac{300}{x+5}$

According to Question

$time_{old}-time_{new} = 2$

$frac{300}{x}- frac{300}{x+5}=2$

$300left [ frac{1}{x}- frac{1}{x+5} right ]=2$

$left [ frac{x+5-x}{x(x+5)} right ]=frac{2}{300}$

$left [ frac{5}{x^2+5x} right ]=frac{1}{150}$

$750=x^2+5x$

$x^2+5x-750=0$

$x^2+30x-25x-750=0$

$x(x+30)-25(x+30)=0$

$(x+30)(x-25)=0$

$either; x= -30 ;or; x=25$

As speed can not be negative so the speed= 25 km/h

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