Problema Solution
A private plane traveled from Seattle to a rugged wilderness, at an average speed of 144 mph. On the return trip, the average speed was 180 mph. If the total traveling time was 8 hours, how far is Seattle from the wilderness?
Answer provided by our tutors
let
v1 = 114 mph the speed of the plane from Seattle to Rugged Wilderness
t1 = time of the trip from Seattle to Rugged Wilderness, t1>0
v2 = 180 mph the speed of the plane from Rugged Wilderness to Seattle
t2 = time of the trip from Rugged Wilderness to Seattle, t2>0
d = the distance from Seattle to Rugged Wilderness
the total traveling time was 8 hours
t1 + t2 = 8
since speed = distance/time => distance = speed*time
v1*t1 = v2*t2
114t1 = 180t2
by solving the system of equations
t1 + t2 = 8
114t1 = 180t2
it is enough to find one of the times t1 or t2
t1 = 240/49 h
click here to see the step by step solution of the system of equations
d = v1*t1
d = 144*(240/49)
d = 705.3 mi
click here to see the step by step calculation
the distance from Seattle to Rugged Wilderness is 705.2 miles.