SOLUTION: Can You Please Help? Here is the question--- A man walked 12km at a certain rate and then 6km farther at a rate of 1 and a half km/hour faster. If he had walked the whole dista

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Question 758663: Can You Please Help?
Here is the question---
A man walked 12km at a certain rate and then 6km farther at a rate of 1 and a half km/hour faster. If he had walked the whole distance at the faster rate, his time would have been 20 minutes less. How long did it really take him to walk the 18km?
Thank You for Your Time :D
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A man walked 12km at a certain rate and then 6km farther at a rate of
1 and a half km/hour faster.
If he had walked the whole distance at the faster rate,
his time would have been 20 minutes less.
How long did it really take him to walk the 18km?
:
let r = "a certain rate"
then
(r+1.5) = the faster rate
:
Change 20 min to 1%2F3 hr
:
Actual time - faster time = 20 min
12%2Fr + 6%2F%28%28r%2B1.5%29%29 - 18%2F%28%28r%2B1.5%29%29 = 1%2F3
Subtract like terms
12%2Fr - 12%2F%28%28r%2B1.5%29%29 = 1%2F3
multiply by 3r(r+1.5)
3(r+1.5)(12) - 3r(12) = r(r+1.5)
(3r + 4.5)(12) - 36r = r^2 + 1.5r
36r + 54 - 36r = r^2 + 1.5r
0 = r^2 + 1.5r - 54
Use the quadratic formula to find r
r+=+%28-1.5+%2B-+sqrt%281.5%5E2-4%2A1%2A-54+%29%29%2F%282%2A1%29+
You can do the math, I got a positive value: r = 6.6366 km/hr
:
Find the time:
t(r) = 12%2F6.6366 + 6%2F%28%286.6366%2B1.5%29%29
t(r) = 1.8 + .74
t(r) = 2.545 hrs
:
:
You can check this by finding the time at the faster rate
18%2F%286.6366%2B1.5%29 Should be .333 hrs less