The first thing we must do is define a variable.
We have then:
x: Linda's speed.
Then, by definition, the time traveled is equal to the distance between the velocity.
We have then:
For Linda:
[tex] t = \frac{10}{x} [/tex]
For Miguel:
[tex] t = \frac{14}{x + 4} [/tex]
Then, since time is the same, then:
[tex] \frac{10}{x} = \frac{14}{x + 4} [/tex]
Clearing Linda's speed we have:
[tex] 10 (x + 4) = 14x [/tex]
[tex] 10x + 40 = 14x [/tex]
[tex] 40 = 14x-10x [/tex]
[tex] 40 = 4x [/tex]
[tex] x = \frac{40}{4} [/tex]
[tex] x = 10 [/tex]
Then, Miguel's speed is:
[tex] x + 4 = 10 + 4 = 14 [/tex]
Answer:
Linda's speed is 10 Km/h
Miguel's speed is 14 Km/h
