Math, asked by wareesha03, 9 months ago

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

Answered by amitnrw
5

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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