Multiple choice

A boy takes 3 hours more when he decreases his speed by 40 miles per hour. If the total distance is 240 miles, what was his actual speed?

  1. 80 miles per hour

  2. 90 miles per hour

  3. 120 miles per hour

  4. 125 miles per hour

  5. 130 miles per hour
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A Correct answer
Explanation

Let speed be v. Time taken at speed v is 240/v. Time taken at speed (v-40) is 240/(v-40). The difference is 240/(v-40) - 240/v = 3. Solving this quadratic equation: 240v - 240(v-40) = 3v(v-40) leads to 9600 = 3v^2 - 120v, or v^2 - 40v - 3200 = 0. Factoring gives (v-80)(v+40) = 0, so v = 80.

AI explanation

Let the actual speed be v miles per hour, so the decreased speed is v - 40 miles per hour. Using the given difference in time, we write the equation 240 / (v - 40) - 240 / v = 3. Solving 240v - 240(v - 40) = 3v(v - 40) yields 9600 = 3v squared - 120v, which simplifies to v squared - 40v - 3200 = 0. Factoring gives (v - 80)(v + 40) = 0, and discarding the negative root leaves the actual speed at 80 miles per hour.

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