When two travellers meet and are two kilometres apart

Towns \(A\) and \(B\) are \(6\) km apart along a straight road. Ali walks from \(A\) towards \(B\) at a constant \(5\) km/h, starting at 9.00 a.m. Bala cycles from \(B\) towards \(A\) at a constant \(15\) km/h, starting at 9.20 a.m., and stops when he reaches \(A\). Let \(t\) be the time in hours after 9.00 a.m.

1. Write down, in terms of \(t\), each traveller’s distance from \(A\), stating the values of \(t\) for which each expression applies. Hence find the time and the place at which they meet.[3]
2. Find the times at which they are exactly \(2\) km apart, explaining why there are no other such times.[4]