Question

Amirah walks at an average speed of (x 1)km/h for x hours and cycles at an average speed of (2x 5)km/h for (x-1) hours. she covers a total distance of 90km. (i)form an equation in x and show that it reduces to 3x2 4x-9=0 (ii)solve the equation 3x2 4x-95=0 (iii)find the time taken for her entire journey

Answer 1

To form the equation, we use the formula for total distance and solve the quadratic equation to find x. Finally, we substitute x into the expression for the total time.

Step-by-step explanation:

To form an equation in x, we can use the formula:
Total distance = Distance walked + Distance cycled
90 = (x * (x + 1)) + ((2x + 5) * (x - 1))
90 = x^2 + x + 2x^2 + 5x - 2x - 5
90 = 3x^2 + 4x - 5
To solve the quadratic equation 3x^2 + 4x - 5 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
x = (-4 ± √(4^2 - 4 * 3 * -5)) / (2 * 3)
x = (-4 ± √(16 + 60)) / 6
x = (-4 ± √76) / 6
x = (-4 ± 2√19) / 6
Finally, to find the time taken for her entire journey, we need to substitute the value of x from the equation into the expression for the total time:
Total time = x + (x - 1)
Total time = 2x - 1