Alfonso runs 10 km at an average speed of x km/h. The next day he runs 12 km at an average speed of (x - 1) km/h.
The time taken for the 10km run is 30 minutes less than the time taken for the 12 km run.
(a) (i)
Write down an equation in x and show that it simplifies to x? – 5x – 20 = 0.

Step-by-step explanation:

Note that t = d/r where t is time, d is distance, and r is rate/speed.

We can come up with two equations with the information given and the equation:

t_1 hr = (10 km)/(x km/hr)

t_2 hr = (12 km)/(x - 1 km/hr)

where t_1 is the time taken to run the 10km the first day and t_2 is the time taken to run the 12km the second day.

We know that 30 minutes is 1/2 of an hour and that t_1 is 30 minutes less than t_2 (as stated in the question). Therefore, we can write:

t_1 = t_2 - 1/2

Substituting the values we derived:

(10 km)/(x km/hr) = (12 km)/(x - 1 km/hr) -1/2

Then we can evaluate by multiplying by 2x(x-1) on both sides:

20(x-1) = 24x - (x)(x-1)

20x - 20 = 24x - x^2 + x

x^2 -5x -20 = 0

And we are done.

I hope this helps! :)

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation: