SOLUTION: Kerry rides a 60km route on his road bike and can average 30km per hour if there is no head or tail wind. For every 5km of wind Kerry's average speed is affected by 1 km/hr. Write

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Question 724073: Kerry rides a 60km route on his road bike and can average 30km per hour if there is no head or tail wind. For every 5km of wind Kerry's average speed is affected by 1 km/hr. Write a rational function that calculates the time, T, it would take Kerry to ride the 60km route with a wind speed of s. How long would it take Kerry to ride the 60km if he was riding into a 30km/hr headwind? Calculate the speed of the wind if it took Kerry 1hour 42mins to ride the 60km route.
I am completely lost to be perfectly honest. This is a distance/speed/time equation. I believe the speed would equal S-1/5? But honestly I'm not even sure where to begin. Any help would be greatly appreciated.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Kerry rides a 60km route on his road bike and can average 30km per hour if there is no head or tail wind.
For every 5km of wind Kerry's average speed is affected by 1 km/hr.
Write a rational function that calculates the time, T, it would take Kerry to ride the 60km route with a wind speed of s.
:
Time = dist/speed
speed = 30 - 1%2F5s
or
speed = 30-.2s
:
T(s) = 60%2F%2830-.2s%29; Time as a function of wind speed
:
How long would it take Kerry to ride the 60km if he was riding into a 30km/hr headwind?
T(s) = 60%2F%2830-.2%2830%29%29
T(s) = 60%2F%2830-6%29
T(s) = 60%2F24
T(s) = 2.5 hrs to ride 60 km with 30km/hr headwind
:
Calculate the speed of the wind if it took Kerry 1hour 42mins to ride the 60km route.
Wait a minute, if there was no wind, it would take 60/30, 2hrs to make the trip
Therefore:
Find the speed of the tail wind, assume 5 km wind adds 1 km/hr
1.7 = 60%2F%2830%2B.2s%29
Multiply both sides by (30+.2s)
1.7(30+.2s) = 60
51 + .34s = 60
.34s = 60 - 51
.34s = 9
s = 26.47 km/hr tail wind to help him ride 60 km in 1 hr 42 min
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