Question

A car travels along a straight line for first half time with a speed of 40 km/h and for the second half time with a speed of 50 km/h.
Find the mean speed of the car,
[Ans. 45 km/h]
​

Answer 1

Solution :

$\sf \: Speed_{1} \: = 40 \: kmph$

$\sf \: Speed_{2} \: = 50 \: kmph$

Let the total time taken by the car be x

Time taken in first half journey = $\sf\dfrac{x}{2}$

Time taken in second half journey = $\sf\dfrac{x}{2}$

Distance Covered in First Half of the Journey :

$\bigstar \: \boxed{ \sf \: Distance_{1} = Speed_{1} \times Time_{1} }$

$\longrightarrow \: \sf \: Distance_{1} = 40 \times \dfrac{x}{2}$

$\longrightarrow \: \sf \: Distance_{1} = \cancel \dfrac{40x}{2}$

$\longrightarrow \: \sf \: Distance_{1} = 20x$

Distance Covered in Second Half of the Journey :

$\bigstar \: \boxed{ \sf \: Distance_{2} = Speed_{2} \times Time_{2} }$

$\longrightarrow \: \sf \: Distance_{2} = 50 \times \dfrac{x}{2}$

$\longrightarrow \: \sf \: Distance_{2} = \cancel \dfrac{50x}{2}$

$\longrightarrow \: \sf \: Distance_{2} = 25x$

Now,

Total Distance Covered = $\sf\: Distance_{1} + Distance_{2}$

→ 20x + 25x = 45x km

Total Time Taken = $\sf\: Time_{1} + Time_{2}$

→ $\sf\dfrac{x}{2} + \dfrac{x}{2}$ = x hours

$\bigstar \: \boxed{ \sf \: Average \: Speed = \frac{Total \: Distance \: Covered }{Total \: Time \: Taken } }$

$\longrightarrow \: \sf \cancel\dfrac{45x}{x}$

$\longrightarrow \: \sf 45 \: kmph$

$\therefore$ Average Speed of car is 45 km/hr.