Multiple choice

A man walks a certain distance with certain speed. If he walks $\dfrac {1}{2}$ km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking

  1. Distance = 45 km, Original speed = 5 km/hr

  2. Distance = 36 km, Original speed = 4 km/hr

  3. Distance = 63 km, Original speed = 7 km/hr

  4. Distance = 72 km, Original speed = 8 km/hr
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B Correct answer
Explanation

Let distance be D and speed be v. D/v - D/(v+0.5) = 1 and D/(v-1) - D/v = 3. Solving these equations yields v = 4 km/hr and D = 36 km.

AI explanation

Using the Time equals Distance divided by Speed formula, we can set up two simultaneous equations based on the given conditions: (D divided by (s + 0.5)) = (D divided by s) - 1 and (D divided by (s - 1)) = (D divided by s) + 3. Solving this system of equations yields the original speed s = 4 km/hr. Substituting this speed back into the equations gives the total distance D = 36 km.

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