### Brain Teasers

# Buses

Every day, Tom walks from home to school, and buses that travel in opposite directions commute on the way at constant intervals. Tom sets off from his home while one bus is just going past him and another bus is coming toward him. Tom arrives at school in 48 minutes while one bus is just going past him and another bus is coming toward him. It's known that buses are 6 times as fast as Tom, and Tom has seen a total of 26 buses on his way.

How long is the time interval between successive buses? Put another way, if you just miss your bus when you arrive at the bus stop, how long would you have to wait until your next bus comes along?

How long is the time interval between successive buses? Put another way, if you just miss your bus when you arrive at the bus stop, how long would you have to wait until your next bus comes along?

### Answer

Let the buses' time interval be t and Tom's walking speed be v.A bus goes past him every 6vt/(6v-v)=6t/5, and a bus comes toward him every 6vt/(6v+v)=6t/7.

Therefore, there are a total of 48/(6t/5)+1=40/t+1 buses that went past him, and 48/(6t/7)+1=56/t+1 buses that came toward him.

40/t+1+56/t+1 implies t=4.

On each bus route, there is a 4 minute interval between buses.

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