The formula of t in terms of s , [tex]v_{1}[/tex] , [tex]v_{2}[/tex] is
[tex]t=\frac{s}{(v_{1}+v_{2})}[/tex]
The value of t when s = 310 , [tex]v_{1}[/tex] = 75 , [tex]v_{2}[/tex] = 80 is 2 hours
Step-by-step explanation:
Two trains left the cities A and B at the same time and headed towards
each other
∵ The cities are s miles apart
∵ After t hours the two trains met each other
∴ s = [tex]s_{1}[/tex] + [tex]s_{2}[/tex], where [tex]s_{1}[/tex] is the
distance that the 1st train moved in t hours and [tex]s_{2}[/tex]
is the distance that the 2nd train moved in t hours
∵ s = v t
∴ [tex]s_{1}[/tex] = [tex]v_{1}[/tex] t
∴ [tex]s_{2}[/tex] = [tex]v_{2}[/tex] t
- Substitute them in the equation of s
∴ s = [tex]v_{1}[/tex] t + [tex]v_{2}[/tex] t
- Take t as a common factor in the right hand side
∴ s = t ( [tex]v_{1}[/tex] + [tex]v_{2}[/tex] )
- Divide both sides by ( [tex]v_{1}[/tex] + [tex]v_{2}[/tex] )
∴ [tex]t=\frac{s}{(v_{1}+v_{2})}[/tex]
The formula of t in terms of s , [tex]v_{1}[/tex] , [tex]v_{2}[/tex] is
[tex]t=\frac{s}{(v_{1}+v_{2})}[/tex]
∵ s = 310 m/h
∵ [tex]v_{1}[/tex] = 75 m/h
∵ [tex]v_{2}[/tex] = 80 m/h
- Substitute these values in the formula of t above
∴ [tex]t=\frac{310}{(75+80)}=\frac{310}{155}[/tex]
∴ t = 2 hours
The value of t when s = 310 , [tex]v_{1}[/tex] = 75 , [tex]v_{2}[/tex] = 80 is 2 hours
Learn more:
You can learn more about distance, speed and time in brainly.com/question/1748290
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