A, B, C are three towns forming a triangle. A man has to walk from one town to the next town, then ride to the next, and then again drive towards his starting point. He can walk, ride, and drive a km in a, b, c minutes respectively. If he starts from B, he takes a + c - b hours, if he starts from C, he takes b + a - c hours, and if he starts from A, he takes c + b - a hours. The length of the triangle is :

A, B, C are three towns forming a triangle. A man has to walk from one

1.	A, B, C are three towns forming a triangle. A man has to walk from one town to the next town, then ride to the next, and then again drive towards his starting point. He can walk, ride, and drive a km in a, b, c minutes respectively. If he starts from B, he takes a + c - b hours, if he starts from C, he takes b + a - c hours, and if he starts from A, he takes c + b - a hours. The length of the triangle is :
Answer» Walking speed of the man `= 60/aa = 60 ` km/h Riding speed of the man `= 60/ba = 60a/b`km/h Driving speed of the man `= 60/c**a = 60a/c`km/h Now, let distance from `B` to `C` is `z` km, distance from `C` to `A` is `y` km, distance from `A` to `B` is `x` km. Then,`z/60+(by)/(60a)+(cx)/(60b) = a+c-b->(1)` `y/60+(bx)/(60a)+(cz)/(60b) = b+a-c->(2)` `x/60+(bz)/(60a)+(cy)/(60b) = c+b-a->(3)` Adding (1),(2) and (3), `(x+y+z)/60+b/(60a)(x+y+z) + c/(60a)(x+y+z) = a+b+c` `=>(x+y+z)/60(1+b/(a)+c/(a)) = a+b+c` `=>(x+y+z)/60((a+b+c)/a) = a+b+c` `=>(x+y+z) = 60a` So, length of triangle is `60a` km.