Two speeds on two mediums, a set distance and set time

Question

to get to the area sidney has to take city streets and the highway. He travels at an average speed of 50km/h on the city streets and an average speed of 100 km/h on the highway. The distance to the arena is 40 km and he made it there in 30 minutes. How long was he on the highway

Answer 1

 

Hi Elena,

Let x and y denote the time spent on the city streets and
that on the highway, respectively.

Then, we get
     x + y = 0.5       (Eq. 1)
as 30 minutes is half an hour.

And, as the travelled distance equals the speed times the time, we get
     50x + 100y = 40   (Eq. 2)

From Eq. 1,
     y = -x + 0.5      (Eq. 3)

If we put Eq. 3 into Eq. 2,
     50x + 100(-x + 0.5) = 40

    -50x + 50 = 40
    -50x = -10
     50x = 10
     x = 0.2

If we put x = 0.2 into Eq. 1, we get
     y = 0.3

0.3 hours is 18 minutes (as 0.3 60 = 18).

 

He was on the highway for 18 minutes.