Question

Two buses A and B leave the same bus depot, A towards the North and B towads the East. The bus A
travels at a speed of 5 km/hr more than that of the bus B. If after four hours the distance between the
two buses is 100 km, find the speed of the bus A.

Answer 1

Answer:

The speed of A = 20 km/hr.

Step-by-step explanation:

Given Problem:

Two buses A and B leave the same bus depot, A towards the North and B towads the East. The bus A  travels at a speed of 5 km/hr more than that of the bus B. If after four hours the distance between the  two buses is 100 km, find the speed of the bus A.

Solution:

Use Pythagorean Theorem,

We know that,

$\bf Rate \times time \sf = distance$

$\sf (4x+20)^2 + (4x)^2 = 100^2\\16x^2 +160x +400 +16x^2 = 10000\\32x^2 +160x -9600 = 0\\x^2 +5x -300 = 0\\(x+20)\times(x-15) = 0$

We have two solutions for x, -20 & 15

We reject the solution  in negative,

x = 15

A = 15 +5 = 20 km/hr                       (Answer)