Question

A journey by car takes \[48\] minutes of \[65\] kmph. How fast the car must go to finish the journey in \[40\] minutes?

Answer 1

Hint: At first, we will find the distance of the journey with help of it further we will calculate the speed of the car using the formula given below

Formula used:We know that, if a car travels with speed v and completes a journey in t time, its distance will be \[v \times t\].
By rearranging the above formula we get \[{\text{v = }}\dfrac{{{\text{distance}}}}{{\text{t}}}\]

Complete step-by-step answer:
It is given that: a car takes \[48\] minutes time to complete a journey when the speed is \[65\]kmph.
We have to find the speed of the car when the same journey has to finish within \[40\]minutes.
At first, we will find the distance of the journey.
We know that, if a car travels with speed v and completes a journey in t time, its distance will be \[v \times t\].
Substitute the value of \[v = 65,t = 48\] we get,
The distance the car travelled is \[ = \dfrac{{65 \times 48}}{{60}}\]kmpm (kilometre per minute)
Here we divide it with $60$ for converting the distance per hour to distance per minute. Because it is given the distance in an hour but we have to calculate the distance in minutes. Therefore we convert the distance of time.
On simplifying the above equation we get the distance covered by the car,
The distance travelled by the car is \[52\] km
Now, the car has to cover \[52\] km within \[40\] minutes.
So, let us substitute the distance and time in the speed formula we get,
Speed=\[\dfrac{{52}}{{40}} \times 60\] kmph (kilometre per hour)
By calculating the above calculation of multiplication and division we get, the speed as \[78\]kmph.
Hence,
The car must go at a speed of \[78\] kmph to finish the journey in \[40\] minutes.

Note:When the distance is the same, the speed and the time will be inversely proportional. It means, it will take less time when then speed is more and vice versa that if speed is less the time taken will be more.