Answered

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?



Answer :

mhanifa

Answer:

  • 70 mph

------------------

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.