suppose a car is driven from town A to town B from town B to town C and from town C to town D which have equal distances at average speeds 20km/hr,60km/hr and 120km/hr respectively,what is the average speed for the whole journey
Time = distance/rate
let the equal distances be x km
individual times are:
x/20, x/60, and x/120 hours
total time = x/20 + x/60 + x/120
= (6x/120 + 2x/120 + x/120)
= 9x/120 hrs
avg speed = total distance/total time
= 3x / (9x/120)
= 40 km/h
To find the average speed for the whole journey, we need to calculate the total distance traveled and the total time taken.
First, let's calculate the distances for each leg of the journey. Since the distances between town A and town B, town B and town C, and town C and town D are equal, let's assume that the distance is d kilometers for each leg.
So, the total distance traveled for the whole journey is:
Total distance = Distance from A to B + Distance from B to C + Distance from C to D
= d + d + d
= 3d kilometers (Eq. 1)
Next, let's calculate the time taken for each leg of the journey.
Time taken from A to B = Distance / Speed = d / 20
Time taken from B to C = Distance / Speed = d / 60
Time taken from C to D = Distance / Speed = d / 120
Now, we can calculate the total time taken for the whole journey:
Total time = Time taken from A to B + Time taken from B to C + Time taken from C to D
= (d / 20) + (d / 60) + (d / 120)
Finally, we can calculate the average speed for the whole journey using the formula:
Average speed = Total distance / Total time
= (3d) / [(d / 20) + (d / 60) + (d / 120)]
Simplifying this expression, we get:
Average speed = (3d) / [(1 / 20) + (1 / 60) + (1 / 120)]
= (3d) / (6/120 + 2/120 + 1/120)
= (3d) / (9/120)
= (3d) / (1/40)
= 120d km/hr
Therefore, the average speed for the whole journey is 120d km/hr.