Two cars on Crete left towns of Knossos and Phaistos at the same time to drive to the other town, passing each other at Gortyns and both travelling at different steady speeds.

The car from Knossos completed the journey from Gortyns to Phaistos in 45 minutes at a steady speed of 64 km/h.

The car from Phaistos completed the journey from Gortyns to Knossos in 20 minutes.

Find the speed of the car from Phaistos.

Source: ask Dr Rob(1997)

Time from P to G = time from K to G.  Time = Distance/speed, so setting those equal for both cars gives Speed of car from P = 64* distance (G to P) / distance (K to G).  Also, we know that the distance from P to G is 64*(.75) hours (45 minutes = .75 hours) and the distance from K to G is the speed of Car P *(1/3) hours (=20 minutes).  Combing those 3 equations gives:
Speed of car P squired, (Vp)^2=2*.75*64^2, or Vp (speed fo car P = 96 kph.

Sorry for the shorthand - I don't type too well and those names are difficult to remember!

Charlie - your algebra is correct (as it nearly always is)!

Edited on October 7, 2013, 8:53 pm

Posted by Kenny M on 2013-10-07 20:53:04