Why didn't the Spartans help the Athenians during the battle of Marathon?

They were having a religious festival at the time and told the Athenians they would be along as soon as it was over. The Athenians lurked in the hills around the plain of Marathon to avoid the superior Persian cavalry while they waited for the Spartan army. However on the tenth day they saw the Persian cavalry being embarked on ships, took the opportunity to run down and defeat the inferior Persian unarmoured infantry without its usual cavalry protection. Having done this, they thought about where the Persian cavalry was going and realised that it was heading for undefended Athens, with traitors ready to open the gates for them as they galloped up from the port.

he Athenian army ran back over the hill the 26 miles to Athens, arriving just as the Persian cavalry was disembarking, and formed up in front of the city walls. Frustrated, the Persians re-embarked and went home. This run by the 9,000 Athenian infantry and their 9,000 light infantry is the origin of today's Marathon run. The Athenians had it much tougher than today's pampered athletes - they ran in sandals and armour carrying their shields and weapons.

The Spartan army left as soon as the festival was over, but arrived a day too late for the battle, marching on to view the battlefield, congratulated the Athenians, and went home.