Cambridge International Mathematics

Formulae and simultaneous equations (Chapter 7) 153

3 When a car travels a distancedkilometres in timethours, the average speedsfor the journey is given

by the formula s=

d

t

km/h.

a Makedthe subject of the formula. Hence find the distance travelled by a car if:

i the average speed is 60 km/h and the time travelled is 3 hours

ii the average speed is 80 km/h and the time travelled is 112 hours

iii the average speed is 95 km/h and the time travelled is 1 h 20 min.

b Maketthe subject of the formula. Hence find the time required for a car to travel:

i 180 km at an average speed of 60 km/h

ii 140 km at an average speed of 35 km/h

iii 220 km at an average speed of 100 km/h.

4 The simple interest$I paid on an investment of$P is determined by the annual rate of interestr

(as a decimal) and the duration of the investment,nyears. The interest is given by the formula

I=P£r£n:

a Makenthe subject of the formula.

biFind the time required to generate$1050interest on an investment of$6400at an interest rate

of8%per annum.

ii Find the time required for an investment of$1000to double at an interest rate of10%per

annum.

When we construct orderivea formula it is often useful to first consider an example with numbers. We can

then generalise the result.

For example, the perimeter of the rectangle is given by

P=3+6+3+6metres

) P=(2£3) + (2£6)metres

) P is double the width plus double the length.

Thus, in general, P=2a+2b

or P=2(a+b):

Example 6 Self Tutor

Write the formula for the total cost RMCof a taxi trip given a fixed charge of:

a RM 3 and RM 0 : 55 per km for 12 km b RM 3 and RM 0 : 55 per km forkkm

c RM 3 and RMdper km forkkm d RMFand RMdper km forkkm

a C=3+(0: 55 £12) b C=3+(0: 55 £k)

) C=3+0: 55 k

c C=3+d£k

) C=3+dk

d C=F+dk

C FORMULA DERIVATION [2.5]

a

b

3m

6m

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Y:\HAESE\IGCSE01\IG01_07\153IGCSE01_07.CDR Tuesday, 14 October 2008 10:40:50 AM PETER