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A motor car does a journey in 17.5 hours, covering the first half at 30 km/h and the second half at 40 km/h. Find the distance of the journey.
- a)684 km
- b)600 km
- c)120 km
- d)540 km
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A motor car does a journey in 17.5 hours, covering the first half at 3...
If the car does half the journey @ 30 kmph and the other half at 40 kmph it’s average speed can be
estimated using weighted averages.
Since, the distance traveled in each part of the journey is equal, the ratio of time for which the car
would travel would be inverse to the ratio of speeds. Since, the speed ratio is 3:4, the time ratio
for the two halves of the journey would be 4:3. The average speed of the car would be:
(30 × 4 + 40 × 3)/7 = 240/7 kmph.
It is further known that the car traveled for 17.5 hours (which is also equal to 35/2 hours).
Thus, total distance = average speed × total time = (240 × 35)/(2 × 7) = 120 × 5 = 600 km
estimated using weighted averages.
Since, the distance traveled in each part of the journey is equal, the ratio of time for which the car
would travel would be inverse to the ratio of speeds. Since, the speed ratio is 3:4, the time ratio
for the two halves of the journey would be 4:3. The average speed of the car would be:
(30 × 4 + 40 × 3)/7 = 240/7 kmph.
It is further known that the car traveled for 17.5 hours (which is also equal to 35/2 hours).
Thus, total distance = average speed × total time = (240 × 35)/(2 × 7) = 120 × 5 = 600 km
Most Upvoted Answer
A motor car does a journey in 17.5 hours, covering the first half at 3...
Given information:
- A motor car does a journey in 17.5 hours.
- The first half of the journey is covered at 30 km/h.
- The second half of the journey is covered at 40 km/h.
To find:
- The distance of the journey.
Solution:
Let the distance of the journey be 'd' km.
Let the time taken to cover the first half of the journey be 't1' hours.
Let the time taken to cover the second half of the journey be 't2' hours.
From the given information, we know the following:
- t1 + t2 = 17.5 (total time taken)
- t1 = d/2 ÷ 30 = d/60 (distance = speed × time)
- t2 = d/2 ÷ 40 = d/80
Substituting t1 and t2 in the first equation, we get:
d/60 + d/80 = 17.5
(4d + 3d)/240 = 17.5
7d = 17.5 × 240
d = 600 km
Therefore, the distance of the journey is 600 km, which is option B.
Note: The solution could be simplified by using the concept of harmonic mean, which gives the average speed of the entire journey as:
2/(1/30 + 1/40) = 2 × 1200/70 = 480/7 km/h
Using the formula distance = speed × time, we get:
distance = (480/7) × 17.5 = 600 km
- A motor car does a journey in 17.5 hours.
- The first half of the journey is covered at 30 km/h.
- The second half of the journey is covered at 40 km/h.
To find:
- The distance of the journey.
Solution:
Let the distance of the journey be 'd' km.
Let the time taken to cover the first half of the journey be 't1' hours.
Let the time taken to cover the second half of the journey be 't2' hours.
From the given information, we know the following:
- t1 + t2 = 17.5 (total time taken)
- t1 = d/2 ÷ 30 = d/60 (distance = speed × time)
- t2 = d/2 ÷ 40 = d/80
Substituting t1 and t2 in the first equation, we get:
d/60 + d/80 = 17.5
(4d + 3d)/240 = 17.5
7d = 17.5 × 240
d = 600 km
Therefore, the distance of the journey is 600 km, which is option B.
Note: The solution could be simplified by using the concept of harmonic mean, which gives the average speed of the entire journey as:
2/(1/30 + 1/40) = 2 × 1200/70 = 480/7 km/h
Using the formula distance = speed × time, we get:
distance = (480/7) × 17.5 = 600 km
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A motor car does a journey in 17.5 hours, covering the first half at 30 km/h and the second half at 40 km/h. Find the distance of the journey.a)684 kmb)600 kmc)120 kmd)540 kmCorrect answer is option 'B'. Can you explain this answer?
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