Xiaohua goes from place A to place B, one-third rides a bike and two-thirds takes a bus. Returning from the second place to the first place, three fifths ride bicycles and two fifths take buses. The result was half an hour late. It is known that riding a bicycle per hour 12 km and taking a bus per hour are 30 km. Q: How many kilometers are there between the two places?

Solution: Take the whole distance as a unit 1.

The difference between the two cycles is 3/5- 1/3=4/ 15.

Speed ratio of cycling and cycling = distance ratio = 30: 12 = 5: 2.

Then the time ratio = 2: 5.

So the time it takes to drive is 2/5 of that of riding a bike.

Then the time required to complete the whole cycle of 4/ 15 by bike = (1/2)/(1-2/5) = 5/6 hours.

Then the time to complete this cycle =(5/6)/(4/ 15)=75/24 hours.

Then the whole journey = 12× 75/24 = 37.5km.

If not, hey, I