Problema Solution
Joe and Nancy decide to take a road trip. The first 75 miles of the drive is pretty easy, while the last 80 miles of the drive is filled with curves. They drove at an average of 7 miles per hour faster for the first 75 miles of the trip. The entire trip took 5 hours. How fast were Joe and Nancy driving for the first 75 miles of the trip?
Answer provided by our tutors
let
d1 = 75 mi
v = the avg. speed the first 75 miles
t = the time needed for the first 75 miles
d2 = 80 mi
v - 7 = the avg. speed the last 80 miles
5 - t = the time needed for the last 80 miles
lets notice that v>7 otherwise v - 7 will be a negative number
since speed=distance/time => distance = speed*time
d1 = v*t
v*t = d1
v*t = 75 divide both sides by v
t = 75/v
d2 = (v - 7)(5 - t)
(v - 7)(5 - t) = 80
plug t = 75/v into the last equation
(v - 7)(5 - 75/v) = 80
by solving we find and consider the root v>7
v = 35 mph
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the first 75 miles of the trip Joe and Nancy we driving with average speed of 35 miles per hour.