A car covers a distance in \(40\) minutes with an average speed of \(60\ km\) per hour. The average speed to cover the same distance in \(30\) minutes is ( )
A car covers a distance in \(40\) minutes with an average speed of \(60\ km\) per hour. The average speed to cover the same distance in \(30\) minutes is ( )
A. \(80\ \frac{km}{h}\)
B. \(\frac {45}{2}\ \frac{km}{h}\)
C. \(70\ \frac{km}{h}\)
D. \(45\ \frac{km}{h}\)
Answer
A
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Solution
Given: Time = \(40\) minutes = \(\frac{40}{60}=\frac23\) hour, Speed =\(60\ km\) per hour. We know that, \(\text{Speed}=\frac{\text{Distance}}{\text{Time}}\). \(\therefore\) Distance covered by a car = \(\text{Speed}\times\text{Time}\)\(=60\ \frac{km}{h}\times\frac{40}{60}\ h\) [\(\because 1\ h=60\) minutes] \(=40\ km\). Now, the average speed to cover the same distance in \(30\) minutes is, \(\text{Speed}=\frac{\text{Distance}}{\text{Time}}\) \(\Rightarrow \text{Speed}=\frac{40\ km}{\frac{30}{60}\ h}\) \(=\frac{60\times40}{30}\ \frac{km}{h}\) \(=2\times40\ \frac{km}{h}\) \(=80\ \frac{km}{h}\) Hence, the average speed to cover the same distance in \(30\) minutes is \(80\ \frac{km}{h}\).
State whether the statement is true (T) or false (F): When two quantities \(x\) and \(y\) are in inverse proportion, then \(\frac {x}{y}\) is a constant.___