Multiple choice

A boy takes 3 hr more if he decreases his speed by 40 km/hr. If the total distance was 240 km, what was his actual speed?

  1. 80 km/hr

  2. 100 km/hr

  3. 120 km/hr

  4. 75 km/hr

  5. None of these
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A Correct answer
Explanation

Let speed be v. Time taken = 240/v. If speed is v-40, time is 240/(v-40). The difference is 240/(v-40) - 240/v = 3. Solving 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 km/hr, so the decreased speed is (v - 40) km/hr. The difference in time taken to travel 240 km is 3 hours, giving the equation 240 divided by (v - 40) minus 240 divided by v equals 3. Multiplying by v(v - 40) yields 9600 = 3 times v times (v - 40), or 3200 = v squared minus 40v. Solving the quadratic equation v squared minus 40v minus 3200 = 0 gives v = 80. The actual speed of the man was 80 km/hr.

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