Question 6
(a) The sum of two numbers is 8 and their product is . Find the numbers.
(b) A truck, P, travelling at 54 kmh passes through a point at 10.30 am while another truck, Q travelling at 90 kmh passes through this same point 30 minutes later. At what time will truck Q overtake P.
Observation
The Chief Examiner reported that majority of the candidates who attempted this question handled it poorly. Many candidate could not able the scale of the graph nor able to the values of the constants.
In part (a), they were expected to let the numbers be a and b.
The sum of numbers gives a + b = 8.. (1).
The product of number gives ab = – 33.. (2). Substituting equation (1) into (2) gives
a (8 – a)= – 33.
Expanding and simplifying gives a2 – 8a – 33 = 0.
Factorizing gives (a + 3)(a – 11) = 0.
Solving gives a = – 3, a = 11 or b = 11, b = -3.
Therefore the numbers are -3 and 11.
In part (b), they were expected to let t = the time, 30 minutes = 1/2 hour.
Then distance travelled by P= 54t …(1). Distance travelled by Q = 90 (t - 1/2)…(2). Solving the equation gives t = 5/4 hours.
The time they met = 10 : 30 + 1hr 15min = 11:45am.