Correct Answer - A
(i) First the car travels a distance of 30 kilometres at a speed of 40 kilometres per hour. Let us find out the time taken by the car to travel this distance.
Here, `" "` Speed = 40 km/h
`" "` Distance = 30 km
And, `" " ` Time = ? `" "` (To be calculated)
We know that, `" "` Speed = `("Distance ")/("Time")`
So, `" "` 40 = `(30)/("Time")`
And, `" "` Time = `(30)/(40)` hours
Or `" "` Time `(t_(1))` = `(3)/(4)` hours `" "` ...(1)
(ii) Next the car travels a distance of 30 km at a speed of 20 km/h. We will also find out the time taken by the car to travel this distance. In this case :
`" "` Speed = 20 km/h
`" "` Distance = 30 km
And, `" "` Time = ? `" "` (To be calculated)
Again, `" "` Speed = `("Distance")/("Time")` ltBrgt So, `" "` 20 = `(30)/("Time")`
And, `" "` Time = `(30)/(20)` hours
Or `" "` Time `(t_(2))` = `(3)/(2)` hours `" "`...(2)
We can get the total time taken by the car for the whole journey by adding the above two time values `t_(1) and t_(2)`. Thus,
`" "` Total time taken = `(3)/(4)+ (3)/(2)` hours
`" " = (3+6)/(4)` hours
`" "= (9)/(4)` hours `" "` ...(3)
And, Total distance travelled = 30 km + 30 km
`" "` = 60 km`" "`...(4)
Now, `" "` Average speed = `("Total distance travelled")/("Total time taken")`
`" "=(60xx4)/(9)`
`" "=(240)/(9)`
`" "` = 26.6 km/h
Thus, the average speed of the car for the whole journey is 26.6 kilometres per hour.
