SOLUTION: The time it takes Karen to drive to work varies inversely with her speed and directly with the square root of the number of red stoplights she encounters. It takes Karen 45 minutes

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Question 1150146: The time it takes Karen to drive to work varies inversely with her speed and directly with the square root of the number of red stoplights she encounters. It takes Karen 45 minutes to get to work if she drives 35 mph and stops at 4 red stoplights. (a) Find the constant of proportionality, k. (b) How long does it take Karen to get to work if she drives 32 mph and stops at 3 red stoplights? Round your answer to the nearest tenth of a minute.
Found 2 solutions by Boreal, ankor@dixie-net.com:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
t=k*sqrt(L)/s
45=k*sqrt(4)/35
1575=2k
k=787.5
t=787.5*sqrt(3)/32
=42.6 min.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The time it takes Karen to drive to work varies inversely with her speed and directly with the square root of the number of red stoplights she encounters.
let t = time to work (in hrs)
let s = vehicle speed
let r = no. of red lights
t+=+%28k%2Asqrt%28r%29%29%2Fs
It takes Karen 45 minutes to get to work if she drives 35 mph and stops at 4 red stoplights.
Change 45 min = .75 hrs
(a) Find the constant of proportionality, k.
%28k%2Asqrt%284%29%29%2F35 = .75
2k = 35(.75)
2k = 26.25
k = 26.25/2
k = 13.125
(b) How long does it take Karen to get to work if she drives 32 mph and stops at 3 red stoplights?
t = %2813.125%2Asqrt%283%29%29%2F32
t = 22.538%2F32
t = .7043 hrs
Round your answer to the nearest tenth of a minute.
.7043(60) = 42.3 minutes