Question

Heena cycles equal distance at speeds x km/h and y km/h and her average speed is 8 km/h.
But when she cycles at these speeds for equal time, she notice her average speed as 9 km/h.
Find the value of x and y for x>y. What value is shown by Heena's act?​

Answer 1

Answer:

x = 12  & y = 6

Step-by-step explanation:

Let say Equal Distance  = D  km

Total Distance = 2D km

Time with x km/h speed = D/x hr

Time with y km/h speed = D/y  hr

Total Time = D/x + D/y  =  D(y + x)/xy  hr

Average speed = Total Distance / Total Time

=>  Total Distance = Average speed * Total Time

=> 2D = 8 * D(y + x)/xy

=> xy = 4(x + y)

Let say Equal time = T  hr

Total time = 2T  hr

Total distance = xT  + yT  = (x + y)T

Average speed =  (x + y)T/2T   = (x + y)/2

9 = (x + y)/2

=> x + y = 18

=> xy = 4(18)

=> xy = 72

xy = 72

x + y = 18

=> x + 72/x = 18

=> x² + 72 = 18x

=> x² - 18x + 72 = 0

=> x² - 6x - 12x + 72 = 0

=> x(x-6) -12(x -6) = 0

=> (x-12)(x-6) = 0

=> x = 12  & 6

& y = 6  & 12

x > y

x = 12  & y = 6