Answer:
Train P : [tex]t_{P} =\frac{330}{55}=6\ \text{hours}[/tex]
Train Q : [tex]t_{Q} =\frac{330}{55}+\frac{1}{2}=6\ \text{hours}\ 30\ \text{minutes}[/tex]
Step-by-step explanation:
The formula to compute the distance traveled by a train is:
[tex]d=s\times t[/tex]
Here,
d = distance traveled
s = speed of the train
t = time taken
From the provided information:
Train P :
d = 330 km
s = x km/h
Then time taken is:
[tex]t=\frac{d}{s}=\frac{330}{x}[/tex]
Train Q :
d = 330 km
s = (x - 5) km/h
[tex]t=\frac{330}{x}+\frac{1}{2}[/tex]
Both the trains traveled the same distance.
[tex]x\times \frac{330}{x}=(x-5)\times [\frac{330}{x}+\frac{1}{2}]\\\\330=\frac{330(x-5)}{x}+\frac{x-5}{2}\\\\330\times 2x=[660(x-5)+x(x-5)]\\\\660x=660x-3300+x^{2}-5x\\\\x^{2}-5x-3300=0\\\\x^{2}+60x-55x-3300=0\\\\x(x+60)-55(x+60)=0\\\\(x-55)(x+60)=0\\\\x=55[/tex]
Compute the time taken by the two trains as follows:
Train P : [tex]t_{P} =\frac{330}{55}=6\ \text{hours}[/tex]
Train Q : [tex]t_{Q} =\frac{330}{55}+\frac{1}{2}=6\ \text{hours}\ 30\ \text{minutes}[/tex]
