Question 1106300: One day Francine drives a total of 21km to work.
Her journey consists of two parts.
For the first part of her journey to work, she drives 15km at
an average speed of x km/h.
a) Write down an expression, in terms of 'x', for the time taken, in hours, for the first 15km.
For the second part of her journey to work, she drives at an
average speed of (x – 27)km/h.
b) Write down an expression, in terms of 'x', for the time taken, in hours, for the second part of the journey.
The total of the times taken by Francine for the two parts of
her journey to work is 40 minutes.
c) Change 40 minutes into hours.
d) Using your answers to a), b), and c), write down an equation in x.
e) Show that this equation simplifies to 2x^2 – 117x + 1215 = 0
f) Hence show that the times taken by Francine for the two parts of her journey to work are the same.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! speed*time=distance
x k/h*t1=15; t1=15/x
(x-27)*t2=6; t2=6/(x-27)
40 minutes =2/3 hour, and t1+t2=2/3
15/x+6/(x-27)=2/3
multiply everything by 3x(x-27) to clear fractions
15*(3*(x-27))+6(3x)=2x(x-27)
15(3x-81)+18x=2x^2-54x
2x^2-54x-45x+1215-18x=0
2x^2-117x+1215=0
(2x-27)(x-45)=0
x=13.5
x=45
only the second can remain positive after subtracting 27
started at 45 k/h and took 20 minutes to go 15 km (1/3 of an hour)
then drove at 18 k/h for 20 minutes, and that is 6 km (1/3 of an hour)
Times are equal.
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