Speed

(i) Cars A and B travel towards one another along a straight road at constant speeds of \(65\text{ km/h}\) and \(50\text{ km/h}\). They pass each other after \(2\) hours.

(i)(a) Find their original separation. (i)(b) Find the time after passing until they are \(460\text{ km}\) apart.

(ii) Cars C and D travel in the same direction along a straight road at constant speeds of \(65\text{ km/h}\) and \(50\text{ km/h}\). C is initially ahead of D and remains ahead. After \(2\) hours their separation is \(55\text{ km}\).

(ii)(a) Find their original separation. (ii)(b) Find the time from the start until they are \(115\text{ km}\) apart.

At the moment when C is \(55\text{ km}\) ahead of D, car E is \(125\text{ km}\) ahead of C and travels towards both cars at a constant \(60\text{ km/h}\).

(ii)(c) Find the interval between E passing C and E passing D. (ii)(d) Find the separation of C and E when E passes D.