two cyclists do the same journey by travelling at 9 km/hr and 10 km/hr respectively. find the distance travelled when one takes 32 minutes longer than the other.

5 days ago 6
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The relevant information found is about two cyclists traveling the same journey at speeds of 9 km/hr and 10 km/hr, with one taking 32 minutes longer than the other. The distance traveled by each cyclist is 48 km. Here is the reasoning:

  • Let the distance traveled be xxx km.
  • Time taken by cyclist at 9 km/hr = x9\frac{x}{9}9x​ hours.
  • Time taken by cyclist at 10 km/hr = x10\frac{x}{10}10x​ hours.
  • The difference in their times is 32 minutes or 3260=0.5333\frac{32}{60}=0.53336032​=0.5333 hours.
  • Equation: x9−x10=0.5333\frac{x}{9}-\frac{x}{10}=0.53339x​−10x​=0.5333.
  • Solving this gives x=48x=48x=48 km.

So, the distance both cyclists travel is 48 km. The slower cyclist takes 32 minutes longer to complete the journey than the faster one.