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A motorist covers a distance of 39 km in 45 min by moving at a speed of x km/h for the first 15 min, then moving at double the speed for the next 20 min and then again moving at his original speed for the rest of the journey. Then, x is equal to:
- a)31.2
- b)36
- c)40
- d)52
- e)53
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A motorist covers a distance of 39 km in 45 min by moving at a speed o...
In the first phase, the motorist travels for 15 minutes at a speed of x km/h. Since distance = speed × time, the distance covered in this phase is given by:
Distance = speed × time = x km/h × (15/60) h = (x/4) km
Distance = speed × time = x km/h × (15/60) h = (x/4) km
In the second phase, the motorist travels for 20 minutes at double the speed of the first phase. So the speed in this phase is 2x km/h. The distance covered in this phase is given by:
Distance = speed × time = 2x km/h × (20/60) h = (2x/3) km
Distance = speed × time = 2x km/h × (20/60) h = (2x/3) km
In the third phase, the motorist travels for the remaining time, which is 45 minutes - 15 minutes - 20 minutes = 10 minutes. The speed in this phase is x km/h, and the distance covered in this phase is:
Distance = speed × time = x km/h × (10/60) h = (x/6) km
Distance = speed × time = x km/h × (10/60) h = (x/6) km
The total distance covered is given as 39 km. So we can add up the distances covered in each phase and set it equal to 39 km:
(x/4) + (2x/3) + (x/6) = 39
(x/4) + (2x/3) + (x/6) = 39
To simplify the equation, we can find a common denominator of 12:
3x + 8x + 2x = 39 × 12
13x = 468
x = 468/13
3x + 8x + 2x = 39 × 12
13x = 468
x = 468/13
Calculating this value, we find:
x ≈ 36
x ≈ 36
Therefore, the value of x is approximately 36 km/h, which corresponds to option B.
Most Upvoted Answer
A motorist covers a distance of 39 km in 45 min by moving at a speed o...
To find the value of x, we need to solve the problem step by step. Let's break it down into smaller parts.
Given:
Distance covered = 39 km
Time taken = 45 min
Step 1: Finding the speed for the first 15 min
Let's assume the speed for the first 15 min is x km/h. As we know, speed = distance/time, we can calculate the distance covered in the first 15 min using this formula:
Distance = Speed * Time
Distance = x km/h * 15 min
Step 2: Finding the speed for the next 20 min
The motorist moves at double the speed for the next 20 min. So, the speed for the next 20 min will be 2x km/h.
Step 3: Finding the speed for the remaining time
The motorist moves at his original speed for the rest of the journey. Since the total journey time is 45 min and the first 15 min and the next 20 min have already been accounted for, the remaining time is 45 min - 15 min - 20 min = 10 min.
Therefore, the speed for the rest of the journey will also be x km/h.
Step 4: Calculating the total distance
The total distance covered is the sum of the distances covered in each time interval.
Total distance = Distance in the first 15 min + Distance in the next 20 min + Distance in the remaining 10 min
Total distance = x km/h * 15 min + 2x km/h * 20 min + x km/h * 10 min
Total distance = 15x + 40x + 10x = 65x km
Step 5: Solving for x
We know that the total distance covered is 39 km.
Therefore, 65x = 39
x = 39/65 = 3/5 km/h
Step 6: Converting the speed to km/h
To convert the speed to km/h, we multiply by 60 (to convert from km/h to km/min) and then by 60 again (to convert from km/min to km/h).
x = (3/5) * 60 * 60 = 36 km/h
Therefore, x = 36 km/h, which corresponds to option B.
Given:
Distance covered = 39 km
Time taken = 45 min
Step 1: Finding the speed for the first 15 min
Let's assume the speed for the first 15 min is x km/h. As we know, speed = distance/time, we can calculate the distance covered in the first 15 min using this formula:
Distance = Speed * Time
Distance = x km/h * 15 min
Step 2: Finding the speed for the next 20 min
The motorist moves at double the speed for the next 20 min. So, the speed for the next 20 min will be 2x km/h.
Step 3: Finding the speed for the remaining time
The motorist moves at his original speed for the rest of the journey. Since the total journey time is 45 min and the first 15 min and the next 20 min have already been accounted for, the remaining time is 45 min - 15 min - 20 min = 10 min.
Therefore, the speed for the rest of the journey will also be x km/h.
Step 4: Calculating the total distance
The total distance covered is the sum of the distances covered in each time interval.
Total distance = Distance in the first 15 min + Distance in the next 20 min + Distance in the remaining 10 min
Total distance = x km/h * 15 min + 2x km/h * 20 min + x km/h * 10 min
Total distance = 15x + 40x + 10x = 65x km
Step 5: Solving for x
We know that the total distance covered is 39 km.
Therefore, 65x = 39
x = 39/65 = 3/5 km/h
Step 6: Converting the speed to km/h
To convert the speed to km/h, we multiply by 60 (to convert from km/h to km/min) and then by 60 again (to convert from km/min to km/h).
x = (3/5) * 60 * 60 = 36 km/h
Therefore, x = 36 km/h, which corresponds to option B.
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Community Answer
A motorist covers a distance of 39 km in 45 min by moving at a speed o...
In the first phase, the motorist travels for 15 minutes at a speed of x km/h. Since distance = speed × time, the distance covered in this phase is given by:
Distance = speed × time = x km/h × (15/60) h = (x/4) km
Distance = speed × time = x km/h × (15/60) h = (x/4) km
In the second phase, the motorist travels for 20 minutes at double the speed of the first phase. So the speed in this phase is 2x km/h. The distance covered in this phase is given by:
Distance = speed × time = 2x km/h × (20/60) h = (2x/3) km
Distance = speed × time = 2x km/h × (20/60) h = (2x/3) km
In the third phase, the motorist travels for the remaining time, which is 45 minutes - 15 minutes - 20 minutes = 10 minutes. The speed in this phase is x km/h, and the distance covered in this phase is:
Distance = speed × time = x km/h × (10/60) h = (x/6) km
Distance = speed × time = x km/h × (10/60) h = (x/6) km
The total distance covered is given as 39 km. So we can add up the distances covered in each phase and set it equal to 39 km:
(x/4) + (2x/3) + (x/6) = 39
(x/4) + (2x/3) + (x/6) = 39
To simplify the equation, we can find a common denominator of 12:
3x + 8x + 2x = 39 × 12
13x = 468
x = 468/13
3x + 8x + 2x = 39 × 12
13x = 468
x = 468/13
Calculating this value, we find:
x ≈ 36
x ≈ 36
Therefore, the value of x is approximately 36 km/h, which corresponds to option B.
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A motorist covers a distance of 39 km in 45 min by moving at a speed of x km/h for the first 15 min, then moving at double the speed for the next 20 min and then again moving at his original speed for the rest of the journey. Then, x is equal to:a)31.2b)36c)40d)52e)53Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A motorist covers a distance of 39 km in 45 min by moving at a speed of x km/h for the first 15 min, then moving at double the speed for the next 20 min and then again moving at his original speed for the rest of the journey. Then, x is equal to:a)31.2b)36c)40d)52e)53Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A motorist covers a distance of 39 km in 45 min by moving at a speed of x km/h for the first 15 min, then moving at double the speed for the next 20 min and then again moving at his original speed for the rest of the journey. Then, x is equal to:a)31.2b)36c)40d)52e)53Correct answer is option 'B'. Can you explain this answer?.
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