Amy and Cole start at the same point and begin skiing in different directions. Amy is skiing west at a speed of 4 miles per hour. Cole is skiing north at a speed of 2 miles per hour.
After how many hours will they be exactly 8 miles apart? Round your answer to two decimal places.

1.79

Step-by-step explanation:

Using the distance formula, we can find the distance between them as a function of time t:

D(t)=(x0−x1)2+(y0−y1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=(−4t−0)2+(0−2t)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=16t2+4t2‾‾‾‾‾‾‾‾‾‾√=20t2‾‾‾‾√=t20‾‾‾√

(Note that we can say t2‾‾√=t and not |t| because in this question t>0). Setting this equal to 8 and solving for t, we find

t20‾‾‾√t=8=820‾‾‾√≈1.79

step-by-step explanation:

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