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4.1 Two aeroplanes leave two different airports, 900km apart from each other, at 9h00 in the
morning. They fly towards each other. The one flies at a speed of 250km/h and the other at
350km/h. At what time will they pass each other? 
4.2 Find the amount of interest that a person will earn if he invests an amount of R8000 for 30
months, at an interest rate of 6% per annum, with the interest compounded semi-annually.
(Leave your answer as an expression in exponential form as you may not use a calculator.
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2 Answers

4.1 Two aeroplanes leave two different airports, 900km apart from each other, at 9h00 in the
morning. They fly towards each other. The one flies at a speed of 250km/h and the other at
350km/h. At what time will they pass each other?
The equation will be:
(900-250t)=350t
It means that the distance to be covered by the first plane will be the same as the second plane has covered, then
600t = 900
t= 1.5 hrs the time will be 10:30
 
The second answer, I agree with the Tutor, In the first I agree with the answer but I like to do things in the most mechanical way.
 
 
 
4.1  First get the speed at which the 2 planes are approaching each other (their relative speed).  This is simply 250 km/hr + 350 km/r = 600 km/hr.  They will meet when the distance that plane 1 covers + the distance covered by plane 2 = 900 km.  Since distance = velocity x time:
 
d = v*t then t = d/v = 900 km/600 km/hr = 1½ hr.  The planes will then meet (pass each other) at 10:30.
 
 
4.2  The formula for calculating compound interest is:  F = P*(1 + i)n , where
 
F = Future value
P = Present value
i = interest rate per compound period
n = number compound periods
 
compounded semi-annually means twice per year or every 6 months.
 
30 ÷ 6 = 5, so n = 5
 
and i = 6 ÷ 2 = 3% per compound period.
 
Then F = $8000 * (1.03).
 
 

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