Question

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 1

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.