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The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?
- a)20 ft
- b)25 ft
- c)750 ft
- d)900 ft
- e)1000 ft
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The circumference of the front wheel of a cart is 30 ft long and that ...
The circumference of the front wheel is 30 ft and that of the rear wheel is 36 feet.
Let the rear wheel make n revolutions. At this time, the front wheel should have made n+5 revolutions.
As both the wheels would have covered the same distance, n*36 = (n+5)*30
36n = 30n + 150
6n = 150
n = 25.
6n = 150
n = 25.
Distance covered = 25*36 = 900 ft.
Most Upvoted Answer
The circumference of the front wheel of a cart is 30 ft long and that ...
Understanding Wheel Circumference and Revolutions
The problem involves two wheels with different circumferences:
- Front wheel circumference: 30 ft
- Back wheel circumference: 36 ft
The relationship between distance traveled and wheel revolutions is crucial here. The distance traveled by a wheel is equal to the number of revolutions multiplied by its circumference.
Revolutions and Distances
Let:
- x = number of revolutions of the back wheel
According to the problem, the front wheel completes five more revolutions than the back wheel:
- Front wheel revolutions = x + 5
Now, let’s determine the distance each wheel travels:
- Distance traveled by the back wheel = x * 36 ft
- Distance traveled by the front wheel = (x + 5) * 30 ft
Setting Distances Equal
Since both wheels are part of the same cart, they travel the same distance:
x * 36 = (x + 5) * 30
Expanding and rearranging gives:
36x = 30x + 150
This simplifies to:
6x = 150
Solving for x gives:
x = 25
Calculating Total Distance
Now, we can find the distance traveled by the cart. Using the number of revolutions of the back wheel:
Distance = 25 revolutions * 36 ft
Distance = 900 ft
Conclusion
Thus, the total distance traveled by the cart when the front wheel has completed five more revolutions than the rear wheel is 900 ft. The correct answer is option D.
The problem involves two wheels with different circumferences:
- Front wheel circumference: 30 ft
- Back wheel circumference: 36 ft
The relationship between distance traveled and wheel revolutions is crucial here. The distance traveled by a wheel is equal to the number of revolutions multiplied by its circumference.
Revolutions and Distances
Let:
- x = number of revolutions of the back wheel
According to the problem, the front wheel completes five more revolutions than the back wheel:
- Front wheel revolutions = x + 5
Now, let’s determine the distance each wheel travels:
- Distance traveled by the back wheel = x * 36 ft
- Distance traveled by the front wheel = (x + 5) * 30 ft
Setting Distances Equal
Since both wheels are part of the same cart, they travel the same distance:
x * 36 = (x + 5) * 30
Expanding and rearranging gives:
36x = 30x + 150
This simplifies to:
6x = 150
Solving for x gives:
x = 25
Calculating Total Distance
Now, we can find the distance traveled by the cart. Using the number of revolutions of the back wheel:
Distance = 25 revolutions * 36 ft
Distance = 900 ft
Conclusion
Thus, the total distance traveled by the cart when the front wheel has completed five more revolutions than the rear wheel is 900 ft. The correct answer is option D.
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The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?a)20 ftb)25 ftc)750 ftd)900 fte)1000 ftCorrect answer is option 'D'. Can you explain this answer?
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