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A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km per hour, he takes 20 minutes more to cover the same distance. The original average speed of the cyclist is
- a)5 km/hour
- b)6 km/hour
- c)7 km/hour
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A cyclist moves non-stop from A to B, a distance of 14 km, at a certai...
Let the original average speed be x
∴ Reduced speed = x - 1
∴ Reduced speed = x - 1
Difference in time = Time taken at average speed (x - 1) - Time taken at average speed x
20/60 = 14/(x - 1) - 14/x [∵ Time = Distance/Speed]
1/3 = 14 × [1/(x - 1) - 1/x]
1/3 = 14/[x(x - 1)]
x(x - 1) = 42
x2 - x - 42 = 0
x2 - 7x + 6x - 42 = 0
x(x - 7) + 6(x - 7) = 0
(x + 6) (x - 7) = 0
x cannot be negative
∴ x = 7 km/hr
1/3 = 14 × [1/(x - 1) - 1/x]
1/3 = 14/[x(x - 1)]
x(x - 1) = 42
x2 - x - 42 = 0
x2 - 7x + 6x - 42 = 0
x(x - 7) + 6(x - 7) = 0
(x + 6) (x - 7) = 0
x cannot be negative
∴ x = 7 km/hr
Most Upvoted Answer
A cyclist moves non-stop from A to B, a distance of 14 km, at a certai...
Let's solve the problem step by step:
1. Initial assumptions:
- Distance between points A and B = 14 km
- Initial average speed = x km/hour
- Reduced average speed = (x - 1) km/hour
- Time taken at initial speed = t hours
2. Calculation of time taken at initial speed:
- Using the formula: Time = Distance/Speed
- Time taken at initial speed: t = 14/x
3. Calculation of time taken at reduced speed:
- Time taken at reduced speed: (t + 1/3) hours (20 minutes = 1/3 hour)
- Distance remains the same, so time = Distance/Speed
- Time taken at reduced speed: 14/(x - 1) = t + 1/3
4. Equation setup:
- From step 2 and step 3, we have:
- 14/x = 14/(x - 1) + 1/3
- Simplifying the equation, we get: x^2 - 7x + 14 = 0
- Solving the quadratic equation, we find x = 7 or x = 2 (Rejecting as it is not possible)
5. Conclusion:
- The original average speed of the cyclist is 7 km/hour (option c)
Therefore, the correct answer is option 'c' - 7 km/hour.
1. Initial assumptions:
- Distance between points A and B = 14 km
- Initial average speed = x km/hour
- Reduced average speed = (x - 1) km/hour
- Time taken at initial speed = t hours
2. Calculation of time taken at initial speed:
- Using the formula: Time = Distance/Speed
- Time taken at initial speed: t = 14/x
3. Calculation of time taken at reduced speed:
- Time taken at reduced speed: (t + 1/3) hours (20 minutes = 1/3 hour)
- Distance remains the same, so time = Distance/Speed
- Time taken at reduced speed: 14/(x - 1) = t + 1/3
4. Equation setup:
- From step 2 and step 3, we have:
- 14/x = 14/(x - 1) + 1/3
- Simplifying the equation, we get: x^2 - 7x + 14 = 0
- Solving the quadratic equation, we find x = 7 or x = 2 (Rejecting as it is not possible)
5. Conclusion:
- The original average speed of the cyclist is 7 km/hour (option c)
Therefore, the correct answer is option 'c' - 7 km/hour.
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A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km per hour, he takes 20 minutes more to cover the same distance. The original average speed of the cyclist isa)5 km/hourb)6 km/hourc)7 km/hourd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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