Mechanics: Vectors Help Needed

**Question**:

Two Ships:

Ship P: t=0; **r**= (20**i** + 30**j**) km, t=3; **r**= (29**i** + 34**j**) km

Ship Q: t=0; **r**= (14**i** - 6**j**) km and **v**=12**j** kmh^-1

at time t hours after midnight, position vectors of P and Q are **p **and **q** km respectively

a) Find velocity of P in terms of **i** and **j**

b) Find expression for **p** and **q** in terms of t, **i** and **j**

c) at time t hours after midnight, distance between P and Q is *d* km

Find expression for PQ to show that

$\displaystyle d^2=25t^2-92t +292$

My answers are as follows:

a) Velocity of P is 3**i** +8**j** kmh^-1

b) **p** = (20** + **3t)**i** + (10+ 8t)**j**

**q** = 14**i** + (12t-6)**j**

c) PQ = (3t - 6)**i** + (4t -16)**j**

Therefore $\displaystyle d^2=(3t-6)^2 + (4t-16)^2$

However, This = $\displaystyle 25t^2 - 164t + 292$

Can anyone see where i have gone wrong, or if the question was wrong to start with?