Problema Solution
A car at a certain speed travels 120 kilometers during the first part. On the second part, it reduces its speed by 10 kph when it travels 100 kilometers. Find the speed on each part of the trip if the whole trip lasted for 4 hours.
Answer provided by our tutors
let
d1 = 120 km the distance of the first part
v1 = the speed on the first part, v1>0
d2 = 100 km the distance of the second part
v2 = the speed on the second part, v2>0
t = 4 hr the total time of the trip
since the average speed = distance/time => time = distance/speed
d1/v1 + d2/v2 = t
120/v1 + 100/v2 = 4
on the second part, the car reduces its speed by 10 kph
v2 = v1 - 10
plug v2 = v1 - 10 into 120/v1 + 100/v2 = 4
120/v1 + 100/(v1 - 10) = 4
by solving we find
v1 = 60 kph
v2 = 10 kph is not a solution since this case v2 = v1 - 10 = 0
click here to see the step by step solution of the equation
v2 = 60 - 10
v2 = 50 kph
the speed on the first part of the trip is 60 kph while the speed on the second part of the trip is 50 kph.