Problema Solution
when fritz drives to work his trip takes 30 minutes, but when he takes the train it takes 20 minutes. Find the distance Fritz travels to work if the train takes an average of 12 miles per hour faster than his driving.
Answer provided by our tutors
let
v = the average speed of driving
v + 12 = the average speed of the train
t1 = 30 min = 30/60 hr = 0.5 hr the time of the travel when driving
t2 = 20 min = 20/60 hr = 1/3 hr the time of the travel with the train
d = the distance of the travel
since average speed = distance/time we have
distance = speed*time
d = v*t
d = v*t1
d = 0.5*v
v = d/0.5
d = (v+12)*t2
d = (v + 12)(1/3)
plug v = d/0.5 into the last equation
((d/0.5) + 12)(1/3) = d
by solving we find
d = 12 mi
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the distance Fritz travels to work is 12 miles.