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John drove from station A to station B a distance of 224 miles. On his way back he increased his speed by 10 mph. If the journey back took him 24 min less, what was his original speed?

User Ashatte
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Answer:

  • 70 mph

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Find the time in travel in both directions, show their difference, considering the distance is 224 and the original speed is s:

  • 224/s - 224/(s + 10) = 24 (time in minutes)
  • 224/s - 224/(s + 10) = 24/60 (time in hours)
  • 224/s - 224/(s + 10) = 2/5

Multiply both sides by 5s(s + 10)/2 and simplify to get quadratic equation:

  • s² + 10s - 5600 = 0
  • s² + 80s - 70s - 5600 = 0
  • s(s + 80) - 70(s + 80) = 0
  • (s - 70)(s + 80) = 0
  • s = 70 and s = - 80

The second root is negative and hence is discarded, hence the answer is 70 mph.

User ZuTa
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