Problema Solution
Lara rode her motorcycle 300 miles. If she averaged 10mph faster, the trip would have taken her 1 hour less time. Find Lara's actual speed. Write an equation and solve.
Answer provided by our tutors
let
v = Lara's actual speed, v>=0
t = the time of the travel with speed v
d = 300 mi the distance traveled
if she averages 10 mph, meaning with speed v + 10 she will take 1 hour less time or t - 1 hours
since distance = speed*time we have
v*t = 300
v = 300/t
(v + 10)(t - 1) = 300
plug t = 300/v into the last equation
(v + 10)(300/v - 1) = 300
by solving we find
v = 50 mph
click here to see the step by step solution of the quadratic equation
Lara's actual speed was 50 mph.