Problema Solution
A private plane traveled from seattle to a rugged wilderness, at an average speed of 182 mph. On the return trip the average speed was 156mph. If the total traveling time was 6 hours, how far is seattle from the Wilderness?
Answer provided by our tutors
let
v1 = 182 mph the average speed from Seattle to Rugged Wilderness
t1 = the traveling time from Seattle to Rugged Wilderness
v2 = 156 mph the average speed from Rugged Wilderness to Seattle
t2 = the traveling time from Rugged Wilderness to Seattle
d = the distance from Seattle to Rugged Wilderness
the total traveling time was 6 hours
t1 + t2 = 6
since average speed = distance / traveling time => distance = average speed * traveling time
d = v1*t1
d = v2*t2
that is
v1*t1 = v2*t2
182*t1 = 156*t2
by solving the system of equations
t1 + t2 = 6
182*t1 = 156*t2
we find
t1 = 36/13 hours
t2 = 42/13 hours
d = v1*t1 = 182*36/13 = 504 miles
the distance from Seattle to Rugged Wilderness is 504 miles.