Two siblings Mark and Steve start from the same point and walk in the same direction at speeds of 5 kilometres per hour and 10 kilometres per hour respectively. After walking for an hour, Mark turns around and walks back along the same path to the starting point. Mark rests for half an hour at the starting point, and then hires a taxi driving at 30 kilometres per hour to catch up with Steve. If the taxi charges $10 for the first 2 kilometres and $2 for every subsequent 500 metres, how much in dollars does Mark pay for the taxi ride?a)92b)102c)142d)152e)160Correct answer is option 'D'. Can you explain this answer?

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Two siblings Mark and Steve start from the same point and walk in the same direction at speeds of 5 kilometres per hour and 10 kilometres per hour respectively. After walking for an hour, Mark turns around and walks back along the same path to the starting point. Mark rests for half an hour at the starting point, and then hires a taxi driving at 30 kilometres per hour to catch up with Steve. If the taxi charges $10 for the first 2 kilometres and $2 for every subsequent 500 metres, how much in dollars does Mark pay for the taxi ride?

a)
92
b)
102
c)
142
d)
152
e)
160

Correct answer is option 'D'. Can you explain this answer?

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Two siblings Mark and Steve start from the same point and walk in the ...

Given:

Speed of Mark = 5 kilometres per hour
Speed of Steve = 10 kilometres per hour
Time after which Mark turns around and walks back = 1 hour
Time for which Mark rests = 0.5 hour
Speed of taxi = 30 kilometres per hour
- Charges for the first 2 kilometres = $10
- Chrages for every subsequent 500 metres = $2

To Find: Amount that Mark paid to the taxi driver?

Approach:

For finding the amount that Mark paid to the taxi driver, we need to find the distance travelled by the taxi.
As the taxi started from the starting point of Steve and stopped when it caught up with Steve, the (Distance travelled by the taxi) = (Distance travelled by Steve since he started walking)
Distance travelled by Steve = Speed of Steve * Time taken
- We are given that speed of steve = 10 kilometres per hour. We need to find the time for which Steve travelled
The travelling time of Steve can be divided into 4 phases:
1. Phase-I: Time for which Mark and Steve both walked = 1 hour
2. Phase-II: Time taken by Mark to reach back the starting point = 1hour
  - As Mark travelled one way for 1 hour and travelled back the same path at the same speed, he will take the same time
  - Please note that Steve kept walking ahead during this time
3. Phase-III: Time for which Mark rests = 0.5 hour
  - Plesae note that Steve kept walking ahead during this time
4. Phase-IV: Time for which the taxi drove = t hours
  1. For this phase, the distance travelled by taxi = total distance travelled by Steve
  2. The time for which the taxi would travel would be equal to the time for which Steve would be travelling in this phase.
  3. As we know the speeds of both taxi and Steve, we can formulate an equation by equating the time taken.
5. We will find the distance travelled by Steve in each of the phases and then sum it up to get the total distance distance travelled by Steve

Working out:

Phase-I: Distance travelled by Steve = 10 * 1 = 10 kilometres
Phase-II: Distance travelled by Steve = 10 * 1 = 10 kilomtres
Phase-III: Disatnce travelled by Steve = 10 * 0.5 = 5 kilomtres
Phase-IV:
- Let the distance covered by Steve in time t hours be x kilometres.
- Total distance covered by taxi to catch up with Steve = 10 + 10 + 5 + x = 25 + x kilometres
  - Time taken by taxi to cover 25 + x kilometres, i.e. t =
- We can equate the time taken by taxi and Steve
So, total distance travelled by the taxi = 25 + 12.5 = 37.5 kilomtres
Charges for the first 2 kilometres = $10
Charges for the rest 35.5 kilomtres = 35.5 * 2 * 2 = $142
Hence, total amount paid to the taxi driver = $10 + $ 142 = $152.

Answer : D

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Most Upvoted Answer

Two siblings Mark and Steve start from the same point and walk in the ...

Given:
- Mark's speed = 5 km/h
- Steve's speed = 10 km/h
- Taxi speed = 30 km/h
- Taxi charges $10 for the first 2 km
- Taxi charges $2 for every subsequent 500 meters

Approach:
1. Calculate the distance traveled by Mark before he turns around.
2. Calculate the time taken by Mark to travel back to the starting point.
3. Calculate the time taken by Steve to travel from the starting point to the point where Mark turned around.
4. Calculate the distance between Mark and Steve when Mark starts taking the taxi.
5. Calculate the time taken by Mark to catch up with Steve using the taxi.
6. Calculate the total cost for the taxi ride.

Calculations:
1. Distance traveled by Mark before turning around:
- Mark's speed = 5 km/h
- Time taken before turning around = 1 hour
- Distance traveled before turning around = Mark's speed * Time taken before turning around
= 5 km/h * 1 hour
= 5 km

2. Time taken by Mark to travel back to the starting point:
- Mark's speed = 5 km/h
- Distance traveled to reach the starting point = 5 km
- Time taken to travel back = Distance traveled / Mark's speed
= 5 km / 5 km/h
= 1 hour

3. Time taken by Steve to travel from the starting point to the point where Mark turned around:
- Steve's speed = 10 km/h
- Time taken by Steve = 1 hour (as both Mark and Steve walk for 1 hour before Mark turns around)

4. Distance between Mark and Steve when Mark starts taking the taxi:
- Distance traveled by Steve = Steve's speed * Time taken by Steve
= 10 km/h * 1 hour
= 10 km
- Distance between Mark and Steve = Distance traveled by Steve - Distance traveled by Mark before turning around
= 10 km - 5 km
= 5 km

5. Time taken by Mark to catch up with Steve using the taxi:
- Taxi speed = 30 km/h
- Time taken by Mark = Distance between Mark and Steve / Taxi speed
= 5 km / 30 km/h
= 1/6 hour

6. Total cost for the taxi ride:
- Cost for the first 2 km = $10
- Cost for the remaining distance (500 meters) = $2 * (Distance traveled by Mark using the taxi - 2 km) / 0.5 km
= $2 * (5 km - 2 km) / 0.5 km
= $2 * 3 / 0.5
= $6

- Total cost for the taxi ride = Cost for the first 2 km + Cost for the remaining distance
= $10 + $6
= $16

The correct option is D) $152.

Answered by Talent Skill Learning · View profile

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Two siblings Mark and Steve start from the same point and walk in the same direction at speeds of 5 kilometres per hour and 10 kilometres per hour respectively. After walking for an hour, Mark turns around and walks back along the same path to the starting point. Mark rests for half an hour at the starting point, and then hires a taxi driving at 30 kilometres per hour to catch up with Steve. If the taxi charges $10 for the first 2 kilometres and $2 for every subsequent 500 metres, how much in dollars does Mark pay for the taxi ride?a)92b)102c)142d)152e)160Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Two siblings Mark and Steve start from the same point and walk in the same direction at speeds of 5 kilometres per hour and 10 kilometres per hour respectively. After walking for an hour, Mark turns around and walks back along the same path to the starting point. Mark rests for half an hour at the starting point, and then hires a taxi driving at 30 kilometres per hour to catch up with Steve. If the taxi charges $10 for the first 2 kilometres and $2 for every subsequent 500 metres, how much in dollars does Mark pay for the taxi ride?a)92b)102c)142d)152e)160Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two siblings Mark and Steve start from the same point and walk in the same direction at speeds of 5 kilometres per hour and 10 kilometres per hour respectively. After walking for an hour, Mark turns around and walks back along the same path to the starting point. Mark rests for half an hour at the starting point, and then hires a taxi driving at 30 kilometres per hour to catch up with Steve. If the taxi charges $10 for the first 2 kilometres and $2 for every subsequent 500 metres, how much in dollars does Mark pay for the taxi ride?a)92b)102c)142d)152e)160Correct answer is option 'D'. Can you explain this answer?.

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