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The time taken by a person to travel an upward distance of $150$ km was $2 \frac{1}{2}$ hours more than the time taken in the downward return journey. If he returned at a speed of $10$ km/h more than the speed while going up, find the speeds in each direction.
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Let the speed in upward direction be 'x' km/h
and the speed in downward direction = $(x + 10)$ km/h
ATQ
$\frac{150}{x} - \frac{150}{x+10} = \frac{5}{2}$
$\Rightarrow x^2 + 10 x - 600 = 0$
$\Rightarrow (x+30)(x - 20) = 0$
$\therefore x = 20$
and $x + 10 = 20 + 10 = 30$
Therefore, speeds in upward and downward direction are $20$ km/h and $30$ km/h respectively.
and the speed in downward direction = $(x + 10)$ km/h
ATQ
$\frac{150}{x} - \frac{150}{x+10} = \frac{5}{2}$
$\Rightarrow x^2 + 10 x - 600 = 0$
$\Rightarrow (x+30)(x - 20) = 0$
$\therefore x = 20$
and $x + 10 = 20 + 10 = 30$
Therefore, speeds in upward and downward direction are $20$ km/h and $30$ km/h respectively.