SOLUTION: 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

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Question 697278: 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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2Fw + 6%2Fc = 1.4
and
5%2Fw + 3%2Fc = 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%2Fw + 6%2Fc = 1.4
2%2F2.5 + 6%2Fc = 1.4
.8 + 6%2Fc = 1.4
6%2Fc = 1.4 - .8
6%2Fc = .6
c = 6/.6
c = 10 mph is the cycling speed
:
:
Check this in the equation: 5%2Fw + 3%2Fc = 2.3
5%2F2.5 + 3%2F10 =
2 + .3 = 2.3