Find the coordinates of the common point of the paths of the two boats.

Show that the boats do not collide.

METHOD 1

\(9{t_A} = 7 - 4{t_B}\) and

\(3 - 6{t_A} = - 6 + 7{t_B}\)     M1A1

solve simultaneously

\({t_A} = \frac{1}{3},{\text{ }}{t_B} = 1\)     A1 

Note: Only need to see one time for the A1.

therefore meet at (3, 1)     A1

[4 marks]

METHOD 2

path of A is a straight line: \(y = - \frac{2}{3}x + 3\)     M1A1 

Note: Award M1 for an attempt at simultaneous equations.

path of B is a straight line: \(y = - \frac{7}{4}x + \frac{{25}}{4}\)     A1

\( - \frac{2}{3}x + 3 = - \frac{7}{4}x + \frac{{25}}{4}{\text{ }}( \Rightarrow x = 3)\)

so the common point is (3, 1)     A1

[4 marks]

METHOD 1

boats do not collide because the two times \(\left( {{t_A} = \frac{1}{3},{\text{ }}{t_B} = 1} \right)\)     (A1)

are different     R1

[2 marks]

METHOD 2

for boat A, \(9t = 3 \Rightarrow t = \frac{1}{3}\) and for boat B, \(7 - 4t = 3 \Rightarrow t = 1\)

times are different so boats do not collide     R1AG

[2 marks]

This was probably the least accessible question from section A. Most started by using the same value of t in attempting to find the common point, and so scored no marks. There were a number of very good candidates who set different parameters for t and correctly obtained (3,1) . There was slightly better understanding shown in part b), though some argued that the boats did not collide because their times were different, yet then provided incorrect times, or even no times at all.

This was probably the least accessible question from section A. Most started by using the same value of t in attempting to find the common point, and so scored no marks. There were a number of very good candidates who set different parameters for t and correctly obtained (3,1) . There was slightly better understanding shown in part b), though some argued that the boats did not collide because their times were different, yet then provided incorrect times, or even no times at all.