Find distance between the two cars at t time

Question

Two cars leave an intersection at the same time. Car A travels north at 55 miles per hour, and Car B travels east at 30 miles per hour. Find the distance (in miles) between the two cars at time t, where t represents the number of minuteselapsed since the cars left the intersection. 

Write your answer as an expression in terms of the variable t.

Answer 1

Car A: 55(t/60) = (11/12)t

Car B: 30(t/60) = (1/2)t

The distance function, per pythagorean, is

sqrt { [(11/12)t ]^2 + [ (1/2)t]^2 } =

sqrt { [ (121/144) t^2 + (1/4) t^2 ] } =

sqrt { [ (121/144)t^2 + (36/144) t^2 ] }

sqrt{ (157/144) t^2 ]

sqrt(157)/ 12 * t

Quick check:

t=1 hour = 60 min

car A is 55 miles north and bar B is mile miles east.

sqrt( 55^2 + 30^2) = sqrt( 3025 + 900) =

sqrt( 3925) = sqrt( 157*25) = 5 * sqrt(157)

Per the formula, for t=60, sqrt(157)/12* 60 = 5 * sqrt(157)

so yes it checks