Problema Solution
a man drove a distance of 80 km at a certain speed returned at a 10 km per hour greater speed. find the rates if the total time consumed was 4 hours.
Answer provided by our tutors
let
v = the speed the man drove 80 km, v>0
d = 80 km the distance he drove in one direction
v + 10 = the return speed (10 km per hour greater speed)
t = 4 hr the total time of the trip
since speed = distance/time follows time = distance/speed
80/v + 80/(v + 10) = 4 multiply both sides by v(v + 10)
80(v + 10) + 80v = 4v(v + 10) divide both sides by 4
20(v + 10) + 20v = v(v + 10)
20v + 200 + 20v = v^2 + 10v
40v + 200 = v^2 + 10v
v^2 - 30v - 200 = 0
by solving we find
v = 35.62 km/hr
click here to see the step by step solution of the equation
v + 10 = 35.62 + 10 = 45.62 km/hr
the man drove with rate of 35.62 km/hr and returned with speed of 45.62 km/hr.