Question

Sriya with her family traveled from Bolpur to Suri by car at a speed of 40km per hour and returned to Bolpur at a speed of 50km per hour. The average speed of the whole journey is

Answer 1

Hint: Now let us assume that the distance between Bolpur and Suri is “d” km. Now we will calculate the time taken to travel from Bolpur to Suri as well as the time is taken to travel from Suri to Bolpur with the help of formula $\text{speed = }\dfrac{\text{Distance}}{\text{Time}}$. Now we will add the timings to find the total time for traveling. Now we have that the average speed is $\dfrac{\text{Total distance}}{\text{Total time}}$ Hence we will substitute the values in the formula and find the average speed.

Complete step-by-step solution:
Now we are given that Sriya with her family traveled from Bolpur to Suri by car at a speed of 40km per hour and returned to Bolpur at a speed of 50km per hour.
Let us say that the distance between Bolpur and Suri is “d” km.
Now we know that the Sriya traveled from Bolpur to Suri at the speed of 40km per hour.
Now we know that $\text{Speed = }\dfrac{\text{Distance}}{\text{Time}}$ .
Hence we have time = $\dfrac{\text{Distance}}{\text{Speed}}$ .
Using this we can say that the time taken to travel from Bolpur to Suri is $\dfrac{d}{40}......................\left( 1 \right)$
Now we are also given that while returning from Suri to Bolpur the speed was 50 km per hour
Hence the time taken to travel from Suri to Bolpur is $\dfrac{d}{50}...................\left( 2 \right)$
Now the total distance traveled in the journey is 2d.
Total time taken for the journey is $\dfrac{d}{40}+\dfrac{d}{50}=\dfrac{50d+40d}{50\times 40}=\dfrac{90d}{2000}$
Hence the total time $\dfrac{90d}{2000}$
Now we know that the average speed is $\dfrac{\text{Total distance}}{\text{Total time}}$ .
Hence we get average speed $=\dfrac{2d}{\dfrac{90d}{2000}}=\dfrac{2\times 2000}{90}=44.44$
Hence we get the average speed = 44.44 km per hour.

Note: Now note that average speed is given by $\dfrac{\text{Total distance}}{\text{Total time}}$ . Hence do not make a mistake by taking the average of the two given speed. If we take the average of given speeds we get $\dfrac{40+50}{2}=\dfrac{90}{2}=45$ . But by solving we get an average speed of 44.44.