Question

An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in \[1\dfrac{2}{3}\]hours, it must travel at a speed of:

Answer 1

Hint: Here first we have to find the distance covered by the aeroplane using the speed and time given. Next using the found distance and the given target time we should find the speed of the aeroplane to reach the distance in the target time.

Formula used: \[{\rm{Distance = Speed \times time}}\]

Complete step-by-step answer:
Here, it is given that the speed of the aeroplane is 240 kmph
And time taken in 5 hours
Now we know that the formula of distance
\[{\rm{Distance = Speed \times time}}\]
Let us now substitute the time and speed of the aeroplane in the distance formula,
Distance \[ = 240 \times 5 = 1200{\rm{ }}km\]
Hence we have found that the distance travelled by the aeroplane is \[1200{\rm{ }}km\]
In question, we should find the speed of the aero plane to cover the same distance in \[1\dfrac{2}{3}\] hours.
We can write \[1\dfrac{2}{3}\]hours as \[\dfrac{5}{3}\]hours.
Now, we have to find the speed of the aeroplane
We apply formula of speed which is being derived from the distance formula,
\[{\rm{Speed = }}\dfrac{{{\rm{Distance}}}}{{{\rm{time}}}}\]
Let us substitute the values of distance and time, we get,
\[{\rm{Speed = }}\dfrac{{{\rm{1200}}}}{{\dfrac{{\rm{5}}}{{\rm{3}}}}}\]
On solving the above equation we can arrive at the required answer,
\[{\rm{Speed = 1200 \times }}\dfrac{{\rm{5}}}{{\rm{3}}}\]
\[{\rm{Speed}} = 720{\rm{ }}km/hr\]
Hence, the aeroplane must travel at a speed of 720 km/hr to cover the distance in the target time.

Additional Information: Speed can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed and covers a relatively large distance in a given amount of time, while a slow-moving object covers a relatively small amount of distance in the same amount of time.

Note: Here the formula of the speed is derived from the known distance formula, we know that the formula of distance is \[{\rm{Distance = Speed \times time}}\], let us divide both sides of the formula by time we get, \[{\rm{Speed = }}\dfrac{{{\rm{Distance}}}}{{{\rm{time}}}}\], similarly we can find the time using the distance formula, let us divide the distance formula by speed on both sides we get, \[{\rm{Time = }}\dfrac{{{\rm{Distance}}}}{{{\rm{Speed}}}}\].