Question

To save the fuel to avoid pollution and good for health the two person A and B are going to their office by riding their bicycle daily 12 km/h. If the speed of B is 2 km/h more than the speed oF A .If a person reaches the office 30minute than A the find the speed of A and B?​

Answer 1

The speed of A = 6 km/hr and the speed of B = 8 km/hr

Step-by-step explanation:

Let the speed of Person A = x km/hr

Therefore the speed of person B = (x + 2)/hr

Person B reaches 30 minutes earlier than A.

the difference of time between reaching office = 30 min.

60 min. =  1 hour

30 min. = $\frac{30}{60}$ = 0.5 hr.

Total distance to the office = 12 km.

$speed=\frac{distance}{time}$

Hence,

$\frac{12}{x}-\frac{12}{x+2} =0.5$

24 = 0.5x² + x

24 - (0.5x² + x) = 0.5x² + x - (0.5x² + x)

-0.5x² - x + 24 = 0

For this equation a = -0.5, b= -1, c = 24 Use quadratic formula

$x=\frac{-(-1)\pm\sqrt{(-1)^2-4(-0.5)(24)} }{2(-0.5)}$

$x=\frac{1\pm(49)}{-1}$

x = -8, 6      speed cannot be in negative number.

so, x = 6 km/hr

and the speed of B = 6 + 2 = 8 km/hr.

The speed of A = 6 km/hr and the speed of B = 8 km/hr

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