Multiple choice

Terry plans a vacation with his friends to travel form Mumbai to Goa. They travel the distance at a speed of 120 km/hr. They decide to come back on a busy weekend due to which they are able to travel at a speed of 90 km/hr. The entire journey took them 7 hours 35 minutes, travelling both ways. How many kilometres they travelled one way?

  1. 390 km

  2. 400 km

  3. 415 km

  4. 545 km

  5. 600 km
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A Correct answer
Explanation

Let distance be d. Time = d/120 + d/90 = 7 hours 35 minutes = 7 + 35/60 = 7 + 7/12 = 91/12 hours. (3d + 4d) / 360 = 91/12. 7d / 360 = 91/12. d = (91 * 360) / (12 * 7) = 13 * 30 = 390 km.

AI explanation

Let the one way distance be d kilometres; using the time formula, time equals distance divided by speed. The total time of 7 hours and 35 minutes converts to 7 and 35/60 hours, or 152/12 hours. The equation is (d/120) + (d/90) = 152/12, which simplifies to (3d + 4d)/360 = 152/12. Solving for d gives 7d/360 = 152/12, so d = (152 multiplied by 360) divided by (12 multiplied by 7), resulting in a one way distance of 390 km.

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