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)
As speed is given in km/h, time is best measured in hours.
The distance between Knossos and Phaistos is the sum of the two parts of the journey: K to G and G to P, regardless of the order.
If x is the number of hours from the time they started out until they met at Gortyns, then
64*(3/4 + x) km = (1/3 + x)*s km
where s is the speed of the car from Phaistos.
And the distance between G and P:
3/4 * 64 = x * s
x = 48 / s
then
48 + 3072/s = (1/3 + 48/s) * s
48 + 3072/s = s/3 + 48
s^2 = 3*3072 = 9216
s = 96 km/h

Posted by Charlie
on 20131007 17:28:46 