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 （ ）
Speed
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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 （ ）
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 \(80\ \frac{km}{h}\).
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 \(80\ \frac{km}{h}\).
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