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An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey?
- a)72
- b)73
- c)74
- d)75
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
An automobile travels from city A to city B and returns to city A by t...
Solution:
Let the distance between city A and city B be 'd'.
Let the time taken during the onward journey be 't1'.
Then, the time taken during the return journey will be 't2' (which is also equal to 't1' as the distance and speed are the same).
Let the average speed for the entire journey be 'v'.
We know that,
distance = speed × time
Onward journey: d = 60 × t1
Return journey: d = 90 × t2
Also, the total distance covered during the entire journey is 2d (as the vehicle travels from A to B and then back to A).
Therefore,
2d = d + d
2d = 60t1 + 90t2
We can simplify this expression to get,
d = 75(t1 + t2)
We want to find the average speed, which is given by the formula:
average speed = total distance / total time
During the entire journey, the total distance covered is 2d and the total time taken is t1 + t2 + t1 + t2 = 2(t1 + t2).
Therefore,
average speed = 2d / 2(t1 + t2)
average speed = d / (t1 + t2)
average speed = 75
Hence, the average speed for the entire journey is 75 km/h.
Therefore, option 'A' is the correct answer.
Let the distance between city A and city B be 'd'.
Let the time taken during the onward journey be 't1'.
Then, the time taken during the return journey will be 't2' (which is also equal to 't1' as the distance and speed are the same).
Let the average speed for the entire journey be 'v'.
We know that,
distance = speed × time
Onward journey: d = 60 × t1
Return journey: d = 90 × t2
Also, the total distance covered during the entire journey is 2d (as the vehicle travels from A to B and then back to A).
Therefore,
2d = d + d
2d = 60t1 + 90t2
We can simplify this expression to get,
d = 75(t1 + t2)
We want to find the average speed, which is given by the formula:
average speed = total distance / total time
During the entire journey, the total distance covered is 2d and the total time taken is t1 + t2 + t1 + t2 = 2(t1 + t2).
Therefore,
average speed = 2d / 2(t1 + t2)
average speed = d / (t1 + t2)
average speed = 75
Hence, the average speed for the entire journey is 75 km/h.
Therefore, option 'A' is the correct answer.
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An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey?a)72b)73c)74d)75Correct answer is option 'A'. Can you explain this answer?
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