Easy #8

The total time to go from Canberra to Sydney, or from Sydney to Canberra, is 210 minutes. By the time the first train reaches the middle of the distance (at 105 minutes after 12 noon), the second train has covered 65 of the 105 minutes it would take to reach the middle, because it begins 40 minutes later. That means that it has a 40- minute diastance from the middle, where the first train is. Given that the two trains travel at the same speed, the will pass at half of that 40-minute distance,which is twenty minutes later than the moment where the first train has reached the middle. So, they will pass 105+20=125 minutes after 12 noon.

The problem is stated in more general case. So, make it a specific case by plugging in values.

Let, Speed of both the train be 30 km/hr.

   Total distance = 30 * 3.5 = 105 km.

After 40 minutes,

   Distance covered = (40/60)30 = (2/3)30 = 20 km.

Remaining distance 85 km will be covered in,

     (85/60)*60 = 85 minutes.

So totally 40 + 85 = 125 min later both will pass each other.

As speed of both is same, Let distance between the two points be 35 km.

then speed of both trains = 35/3.5 = 10 km/hr.

Let the trains meet after time t hr after 12:00 hr. then train form Canberra travels a distance of 10 × t = 10t km. and

then train form Syndey travels a distance of 10 × (t – 40/60) = (10t + 20/3) km. as it started 40 minutes late.

so 10t + 10t + 20/3 = 35

20t = 35 – 20/3 = 125/3 or t = 125/3 hr = 2 1/12 hr = 2 hr 5 min = 125 minutes