The first thing we are going to do for this case is to define a variable.
x: speed of the trolley
Then, by definition we have to:
[tex]t = d / v
[/tex]
Where,
t: time
d: distance
v: speed
For the bus we have:
[tex]t = 90 / (x + 6)
[/tex]
For the trolley we have:
[tex]t = 75 / x
[/tex]
Since the time is the same then we have:
[tex]90 / (x + 6) = 75 / x
[/tex]
From here, we clear the value of x:
[tex]90x = 75 (x + 6)
90x - 75x = 450
25x = 450
x = 450/25
x = 18[/tex]
So, the speed of the trolley is:
[tex]x = 18 m / h
[/tex]
The bus speed is:
[tex]x + 6 = 18 + 6 = 24 m / h
[/tex]
Answer:
Trolley: 18 m / h
Bus: 24 m / h
