Shortcut Trick
Total time for the journey = 750 ÷ 50 = 15 hours.
Time spent on the first 200 km = 200 ÷ 40 = 5 hours.
Remaining time for the next 550 km = 15 − 5 = 10 hours.
Required speed for remaining distance = 550 ÷ 10 = 55 kmph.
∴ The correct answer is 55 kmph.
Alternate Method
Given:
Total distance = 750 km
Distance of 1st part = 200 km, Speed of 1st part = 40 kmph
Distance of 2nd part = 550 km
Overall average speed = 50 kmph
Formula Used:
Average Speed = Total Distance ÷ Total Time
Speed = Distance ÷ Time
200 km
550 km
Total Distance: 750 km (Avg Speed: 50 kmph)
Speed = 40 kmph
Time = 5 hrs
Speed = ? kmph
Time = 10 hrs
Calculations:
⇒ Total Time = Total Distance ÷ Average Speed
⇒ Total Time = 750 ÷ 50 = 15 hours
⇒ Time taken for the first 200 km = Distance ÷ Speed = 200 ÷ 40 = 5 hours
⇒ Time remaining for the next 550 km = Total Time − Time taken for the first part
⇒ Time remaining = 15 − 5 = 10 hours
⇒ Required speed for the next 550 km = Distance ÷ Time
⇒ Required speed = 550 ÷ 10 = 55 kmph
∴ The correct answer is 55 kmph.
Additional Information
Average Speed
Average speed is the total distance traveled divided by the total time taken. It is not simply the arithmetic mean of the different speeds.
Average Speed for Equal Distances
If an object covers two equal distances at speeds x and y, the average speed over the entire journey is directly calculated using the formula 2xy ÷ (x + y).
Relative Speed
When two objects move in opposite directions, their relative speed is the sum of their individual speeds. When moving in the same direction, it is the difference between their individual speeds.