Multiple choice

A truck covers a distance of 384 km at a certain speed. If the speed is decreased by 16 km/h, it will take 2 hours more to cover the same distance. 75% of its original speed (in km/h) is

  1. 45

  2. 54

  3. 48

  4. 42
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed be v. 384/(v-16) - 384/v = 2. Solving for v: 384v - 384(v-16) = 2v(v-16). 384 * 16 = 2v^2 - 32v. v^2 - 16v - 3072 = 0. Roots are (16 +/- sqrt(256 + 12288))/2 = (16 +/- 112)/2. v = 64. 75% of 64 is 48.

AI explanation

Using the basic formula time equals distance divided by speed, let the original speed be v km/h. The equation for the given condition is 384 divided by (v minus 16) minus 384 divided by v equals 2. Multiplying by v multiplied by (v minus 16) gives 384v minus 384 multiplied by (v minus 16) = 2v squared minus 32v, which simplifies to v squared minus 16v minus 3072 = 0. Factoring this quadratic equation gives (v minus 64)(v + 48) = 0, so the original speed is 64 km/h. Calculating 75 percent of 64 gives the final answer of 48 km/h.

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