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A car starts running with the initial speed of 20 km/h and its speed increases every hour by 4 km/h. How many hours will it take to cover a distance of 504 km?
- a)4
- b)8
- c)12
- d)16
Correct answer is option 'C'. Can you explain this answer?
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Solution:
Given, initial speed of the car = 20 km/h
Increase in speed every hour = 4 km/h
Let the time taken to cover a distance of 504 km be 't' hours
Distance covered by the car in 't' hours = 20t + 4(1+2+3+...+(t-1)) [Using the formula for sum of first 'n' natural numbers]
= 20t + 4×(t-1)×(t-1+1)/2
= 20t + 2×(t-1)×t
= 20t + 2t(t-1)
= 2t² + 18t
We need to find 't' such that the distance covered by the car is 504 km
Therefore, 2t² + 18t = 504
Simplifying, we get t² + 9t - 252 = 0
On solving this quadratic equation, we get t = 12 (as t > 0)
Therefore, the car will take 12 hours to cover a distance of 504 km.
Answer: Option C.
Given, initial speed of the car = 20 km/h
Increase in speed every hour = 4 km/h
Let the time taken to cover a distance of 504 km be 't' hours
Distance covered by the car in 't' hours = 20t + 4(1+2+3+...+(t-1)) [Using the formula for sum of first 'n' natural numbers]
= 20t + 4×(t-1)×(t-1+1)/2
= 20t + 2×(t-1)×t
= 20t + 2t(t-1)
= 2t² + 18t
We need to find 't' such that the distance covered by the car is 504 km
Therefore, 2t² + 18t = 504
Simplifying, we get t² + 9t - 252 = 0
On solving this quadratic equation, we get t = 12 (as t > 0)
Therefore, the car will take 12 hours to cover a distance of 504 km.
Answer: Option C.
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