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# word problems

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.

### 2 Answers by Expert Tutors

Francisco E. | Francisco; Civil Engineering, Math., Science, Spanish, Computers.Francisco; Civil Engineering, Math., Sci...
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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?
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.

Stephen K. | Physics PhD experienced in teaching undergraduatesPhysics PhD experienced in teaching unde...
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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).