Carol walks 12 km at x km/h and then a further 6 km at (x-1) km/h.
The total time taken is 5 hours.
(i) write an equation in terms of x and show that it simplifies to 5x^2-23x+12=0
(ii) factorise -5x^2-23x+12=0
(iii) solve the equation 5x^2-23x+12=0
(iv) write down carols walking speed during the final 6 km
Answers
Given : Carol walks 12 km at x km/h and then a further 6 km at (x-1) km/h.
The total time taken is 5 hours.
To Find :write an equation in terms of x and show that it simplifies to 5x^2-23x+12=0
Solution:
Time = Distance / Speed
Carol walks 12 km at x km/h
Hence Time = 12/x hr
further 6 km at (x-1) km/h
further time = 6/(x - 1) hr
Total Time = 12/x + 6/(x - 1) hr
Total time = 5 hr
Equate
=> 12/x + 6/(x - 1) = 5
=> 12(x - 1) + 6x = 5x(x-1)
=> 12x - 12 + 6x = 5x² - 5x
=> 5x² - 23x + 12 = 0
Factorize
5x² - 20x - 3x + 12 = 0
=> 5x(x - 4) - 3(x - 4) = 0
=> (5x - 3) (x - 4) = 0
=> x = 3/5 , x = 4
x = 3/5 not possible as then x - 1 would be -ve
Hence x = 4
x - 1 = 3
carols walking speed during the final 6 km = 3 km/hr
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