(a) If x m is the length of each straight and y m the radius of each semicircular end, fi nd an expression for the perimeter P, in terms of x and y.
(b) If x = 100 m and y = 31⋅85 m, fi nd the perimeter to the nearest metre.
(c) If a runner has an average speed of 30 km/h, how long does it take the runner to complete one full circuit of the track?
9
A running track has two straights and two semicircular ends, as shown.
x m Straight C
Solution (a) 1. The quantity is the perimeter P. 2. The diagram is given. x
y y
x 3. There are two variables: x and y.
4. P = 2x + 2πy [2πy is the circumference of a circle of radius y.]
(b) P = 2(x) + 2π( y) Filling in x = 100 and y = 31·85 gives: P = 2(100) + 2π(31⋅85) = 400 m
(c) Speed = 30 km/h [Be careful with the units.] = 30 × 1000 m
___________ 3600 s
= 25 __
3 m/s
Time = Distance ________
Speed
= 400 ____
__ 3
EXERCISE 3
1. An entrepreneur bought x phones at € 30 each and sold y of them at € 98 each. By copying and completing the table, fi nd the entrepreneurʼs net profi t in terms of x and y.
Sold Bought
Number of phones Price/unit Total
2. An L-shaped fl owerbed is shown with | DC | = x m and | CB | = y m. If [AB] is 1 m longer than [CD] and [ED] is 2 m longer than [CB], fi nd expressions for:
(a) perimeter P, (b) area of the fl owerbed, in terms of x and y.
