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Jonathan drove from City A to City B at a rate of 1.2 minutes per kilometer. He then drove back to City A from City B , along the same route, at 1 minute per kilometer. If he took anywhere between 3 hours to 5 hours to travel from City A to City B and between 2 hours to 3 hours on his way back, what could be the distance between the two cities?
  • a)
    140 kilometers
  • b)
    160 kilometers
  • c)
    200 kilometers
  • d)
    220 kilometers
  • e)
    270 kilometers
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Jonathan drove from City A to City B at a rate of 1.2 minutes per kilo...
Jonathan drove from A to B at a rate of 1.2 min per km. He drove between 3 and 5 hours.
t = 3 h = 180 min which is equivalent to 150 km, (You can eliminate A, the minimum value is 150, 140 is out of range)
t = 5 h = 300 min, which is equivalent to 250 km (You can eliminate E, the maximal value is 250, 270 is also out of range)

On the way back Jonathan takes one minute to drive each km.
The trip takes between 2 to 3 hours, so he must have drove between 120 to 180 km. C and D are also out of range, the only possible answer is B
. Jonathan drove 160 km, it is the only value that belongs to both the ranges.
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Most Upvoted Answer
Jonathan drove from City A to City B at a rate of 1.2 minutes per kilo...
Given:

- Jonathan drove from City A to City B at a rate of 1.2 minutes per kilometer.
- He then drove back to City A from City B, along the same route, at 1 minute per kilometer.
- He took anywhere between 3 hours to 5 hours to travel from City A to City B.
- He took between 2 hours to 3 hours on his way back.

To find:

- The distance between the two cities.

Approach:

- Use the formula: Distance = Speed x Time
- Convert the given rates to km/min.
- Use the given time ranges to form inequalities and solve for distance.

Solution:

Converting rates to km/min:

- Rate from A to B = 1/1.2 = 0.833 km/min
- Rate from B to A = 1/1 = 1 km/min

Let the distance between A and B be d km.

Using the formula, Distance = Speed x Time:

- Time taken from A to B = d x 0.833 = 0.833d minutes
- Time taken from B to A = d x 1 = d minutes

Using the given time ranges to form inequalities:

- 3 hours = 180 minutes ≤ 0.833d ≤ 300 minutes = 5 hours
- 2 hours = 120 minutes ≤ d ≤ 180 minutes = 3 hours

Solving for d:

- 180/0.833 ≤ d ≤ 180/0.5
- 216 ≤ d ≤ 360

The only option that falls within this range is option B, 160 kilometers.

Therefore, the distance between City A and City B is 160 kilometers.
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Community Answer
Jonathan drove from City A to City B at a rate of 1.2 minutes per kilo...
Very good qn of could be true kind
main catch is the speed ratio are 50:60 kmph
so the range is 120- 180 km
but if A-B shows the range of 150-250 km
and if you choose 140 then it ll violate A-B clause
so 140 will eliminated and 160 is considered the answer.
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Jonathan drove from City A to City B at a rate of 1.2 minutes per kilometer. He then drove back to City A from City B , along the same route, at 1 minute per kilometer. If he took anywhere between 3 hours to 5 hours to travel from City A to City B and between 2 hours to 3 hours on his way back, what could be the distance between the two cities?a)140 kilometersb)160 kilometersc)200 kilometersd)220 kilometerse)270 kilometersCorrect answer is option 'B'. Can you explain this answer?
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