<PRE><B>Question 697278</B>
If Mr. Norton walks for 2 miles and then cycles for 6 miles, it takes him 1 hr and 24 min to go the total distance of 8 miles
....but if he walks for 5 miles and cycles for 3 miles the rates of walking and cycling being the same as before, the total time taken is 2 hr and 18 min.
 Find the rates of walking and cycling.
:
let w = his walking speed
let c = cycling speed
:
change 1 hr 24 min to: 1 + 24/60 = 1.4 hrs
change 2 hr 18 min to: 2 + 18/60 + 2.3 hrs
:
Write time equation for scenario
{{{2/w}}} + {{{6/c}}} = 1.4
and
{{{5/w}}} + {{{3/c}}} = 2.3
:
multiply the above equation by 2wc and mult the 1st equation by wc
10c + 6w = 4.6wc
 2c + 6w = 1.4wc
--------------------subtraction eliminates w, find c
8c = 3.2wc
divide both sides by c
8 = 3.2w
w = 8/3.2
w = 2.5 mph walking speed
:
Find the cycling speed using eq: {{{2/w}}} + {{{6/c}}} = 1.4
{{{2/2.5}}} + {{{6/c}}} = 1.4
.8 + {{{6/c}}} = 1.4
{{{6/c}}} = 1.4 - .8
{{{6/c}}} = .6
c = 6/.6
c = 10 mph is the cycling speed
:
:
Check this in the equation: {{{5/w}}} + {{{3/c}}} = 2.3
{{{5/2.5}}} + {{{3/10}}} = 
2 + .3 = 2.3</PRE>