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A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, then the first speed of the truck was of

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60 km/hr

63 km/hr

61 km/hr

62 km/hr

answer is A.

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Detailed Solution

Given that a truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed.
Let's assume that the initial speed of the truck was

p

km/hr then,
Final speed of the truck

= (p + 20)

km/hr.
Then,
Time taken to cover the distance with the initial speed,

t_{1} = \frac{150}{p}

\{time = \frac{distance}{speed}\}

Time taken to cover the distance with the final speed,

t_{2} = \frac{200}{p + 20}

hr
According to the given condition,

⟹ \frac{150}{p} + \frac{200}{p + 20} = 5

⟹ \frac{150 (p + 20) + 200 p}{p (p + 20)} = 5

⟹ 150 p + 3000 + 200 p = 5 (p^{2} + 20 p)

⟹ 150 p + 3000 + 200 p = 5 p^{2} + 100 p

⟹ 5 p^{2} + 100 p - 200 p - 150 p - 3000 = 0

⟹ 5 p^{2} - 250 p - 3000 = 0

⟹ p^{2} - 50 p - 600 = 0

⟹ p^{2} - 60 p + 10 p - 600 = 0

⟹ p (p - 60) + 10 (p - 60) = 0

⟹ (p + 10) (p - 60) = 0

⟹ p + 10 = 0 or p - 60 = 0

∴ p = - 10 or p = 60

Speed of the truck cannot be negative.
∴ The initial speed of the truck is 60 km/hr.
Hence, option (1) is correct.

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