SOLUTION: I have to walk a distance of 24km. If I increase my usual rate of walking by 2km/h, I can reduce the time taken by 1 hour. a) find my usual rate of walking b) if I can reduce my

Let "r" be your usual rate, and t be the time to walk 24 km at this rate.


Then

rt = 24                 (1)
(r+2)*(t-1) = 24.       (2)


Transform eq(2) in this way:

rt + 2t - r - 2 = 24.   (3)


Take into account that 24 = rt in accordance with (1).  So you can cancel the terms rt and 24 in both sides of the equation (3) to get

2t - r - 2 = 0,   or simply   r = 2t-2 = 2*(t-1).


Next substitute this expression for r,  r = 2*(t-1),  into eq(1)  to get

2(t-1)*t = 24,   or  t*(t-1) = 12.


Further, you can solve the last equation for t  as a quadratic equation,  or simply "to guess" the solution t = 4.


So, the answer to the question  a)  is   t = 4 hours  (your usual time)  and  r =  = 6 km/h  (your usual rate).



Having this, you can easily resolve b) on your own.