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# A car travelling with $\frac{2}{3}$ rd of its actual speed, covers 42 miles in 1 hr 30 min 10 sec. What is the actual speed of the car ?

$\begin{array}{1 1} (a)\; 50\; miles/hr \\(b)\; 48\; miles/hr \\(c)\; 46\;miles/hr \\ (d)\; 42\; miles/hr \end{array}$

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A)
$Time = 1 \;hr \;30\;min\;10\;sec$
$\qquad = 1 + \frac{30}{60} + \frac{10}{3600}$
$\qquad =1 + \frac{1}{2} + \frac{1}{360}$
$\qquad = \frac{360+180+1}{360}$
$\qquad = \frac{541}{360}$
Distance = $42 \;miles$
$Speed = \frac{distance }{time}$
$Speed = \frac{42}{541/360}$
$\qquad = \frac{42 \times 360}{541}$
$\qquad = \frac{15120}{541}$
$\qquad = 27.94 \;\; \cong 28$
$\frac{2}{3}^{rd} of\; the \;speed = 28$
$\therefore Actual \;speed = 28 \times \frac{3}{2} = 42\; miles/hr$