Question

Distance between two cities A and B is 425km. If a car leaves A at 2 PM and reaches B at 10:30 PM, then what is the speed of the car?

Answer 1

Hint: To find the speed of the car, when the distance travelled and time taken by it is given, use the formula:
$\text{Speed =}\dfrac{\text{Total distance travelled}}{\text{Total time taken}}$
We have to find the total time taken to cover the required distance in hours and then we can apply the formula to get the speed.

Complete step-by-step solution -
Total distance between city A and city B = 425 km.
Since, 1 km = 1000 m
Hence, Total distance = 425 km
$\begin{align}
  & =\left( 425\times 1000 \right)m \\
 & =4,25,000m \\
\end{align}$
Total time taken = (Time at which it reaches B – Time at which it has started from A)
Total time taken = (10:30 – 2:00) hrs
= 8:30 hrs
= 8 hours 30 minutes
Now, we have to convert 8 hours 30 minutes into hours;
$\Rightarrow 8\text{ }hours\text{ }30\text{ }minutes=8\ hours+\left( \dfrac{30}{60} \right)hrs$
Since, 1 hour = 60 minutes
i.e. 60 minutes = 1 hours
$\begin{align}
  & 1\ \text{minute }=\dfrac{1}{60}hours \\
 & \Rightarrow 30\ \text{minutes }=\dfrac{30}{60}hours=\dfrac{1}{2}hours \\
\end{align}$
$\text{Total time taken =}\left( 8+\dfrac{1}{2} \right)hours=\left( \dfrac{17}{2} \right)hours$
Now, we can put the value of distance in km and time in hours in the formula.
$\begin{align}
  & \therefore \text{speed = }\dfrac{\text{Distance}}{\text{Time}} \\
 & speed=\dfrac{425km}{\left( \dfrac{17}{2} \right)hr} \\
 & speed=\left( \dfrac{425\times 2}{17} \right)km/hr=\left( \dfrac{850}{17} \right)km/hr \\
 & speed=50km/hr \\
\end{align}$
We can also calculate speed in metre / second by putting the value of distance in metres and time in seconds.
We, have distance = 4,25,000 metres
Time taken $=\left\{ \left( Time\ in\ hours \right)\times 60\times 60 \right\}\sec $
Since, 1 hour = 60 minutes
And 1 minutes = 60 seconds
$\begin{align}
  & \therefore 1\ \text{hours}=\left( 60\times 60 \right)\text{seconds} \\
 & \therefore \text{Time taken }\left( \text{in seconds} \right)=\left( \dfrac{17}{2}\times 60\times 60 \right)\text{seconds} \\
 & \therefore \text{Speed }\left( \text{in m/s} \right)=\dfrac{\text{Distance }\left( \text{in metres} \right)}{\text{Time}\left( \text{in seconds} \right)} \\
 & \text{Speed =}\dfrac{4,25,000}{\left( \dfrac{17}{2}\times 60\times 60 \right)} \\
 & \text{Speed =}\dfrac{4,25,000\times 2}{17\times 60\times 60}=\dfrac{8,50,000}{17\times 60\times 60}=\dfrac{50,000}{60\times 60} \\
 & \text{Speed =}\dfrac{500}{36}=\dfrac{125}{9}\text{m/second} \\
\end{align}$

Note: Instead of converting the distance given in kilometres into metres and time taken given in hours into seconds and then calculating speed in metre per second, we can directly calculate speed in kilometre per hour and then convert it into metre per second, using formula:
\[\text{Speed in metre/second = }\dfrac{5}{18}\times \left( \text{Speed in kilometre/hour} \right)\]