Question

A truck covers a distance of 384 km at a certain speed. If the speed is reduced by 16 km / h, it will take two hours more to cover the same dis

Answer 1

75% of the original speed of the truck which covers a distance of 384 km is 48 km/hr.

Explanation:

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Q. A truck covers a distance of 384 km at a certain time. If the speed is reduced by 16 km / h, it will take two hours more to cover the same distance. What is 75% of its original speed (in km/hr)?

Required formula:

• Time = [Distance] / [Speed]

The distance covered by the truck = 384 km

Let the original speed of the truck be “s” km/hr.

Therefore,

Time taken by the truck with the original speed = $\frac{384}{s}$  hr

And,

Time taken  by the truck with the reduced speed = $\frac{384}{(s-16)}$ hr

Now, according to the question, we can write the eq. as,

$\frac{384}{(s-16)}$ – $\frac{384}{s}$ = 2

⇒ 384 [$\frac{s-s+16}{s(s-16)}$] = 2

⇒ 192 * 16 = s² – 16s

⇒ s² – 16s – 3072 = 0

⇒ s² – 64s + 48s – 3072 = 0

⇒ s(s-64) + 48(s-64) = 0

⇒ (s-64)(s+48) = 0

⇒ s = 64 or – 48

Neglecting the negative value

⇒ s = 64  km/hr ← the original speed of the truck

 

Thus,  

75% of the original speed of the truck is given by,

= (75/100) * 64

= 0.75 * 64

= 48 km/hr

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