Question

Two trains left the cities A and B at the same time and headed towards each other. The cities are s miles apart. The first train was traveling at the speed of v1 mph. The second train was traveling at the speed of v2 mph. After t hours the two trains met each other. Find the formula for t in terms of s,v1 and v2. Then find the value of t if: s=310, v1 = 75, v2 = 80

Answer 1

The formula of t in terms of s , $v_{1}$ , $v_{2}$ is

$t=\frac{s}{(v_{1}+v_{2})}$

The value of t  when s = 310 , $v_{1}$ = 75 , $v_{2}$ = 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
• The first train was traveling at the speed of $v_{1}$ mph
• The second train was traveling at the speed of $v_{1}$ mph
• After t hours the two trains met each other

∵ The cities are s miles apart

∵ After t hours the two trains met each other

∴ s = $s_{1}$ + $s_{2}$, where $s_{1}$ is the

   distance that the 1st train moved in t hours and $s_{2}$

    is the distance that the 2nd train moved in t hours

∵ s = v t

∴ $s_{1}$ = $v_{1}$ t

∴ $s_{2}$ = $v_{2}$ t

- Substitute them in the equation of s

∴ s = $v_{1}$ t + $v_{2}$ t

- Take t as a common factor in the right hand side

∴ s = t ( $v_{1}$ + $v_{2}$ )

- Divide both sides by ( $v_{1}$ + $v_{2}$ )

∴ $t=\frac{s}{(v_{1}+v_{2})}$

The formula of t in terms of s , $v_{1}$ , $v_{2}$ is

$t=\frac{s}{(v_{1}+v_{2})}$

∵ s = 310 m/h

∵ $v_{1}$ = 75 m/h

∵ $v_{2}$ = 80 m/h

- Substitute these values in the formula of t above

∴ $t=\frac{310}{(75+80)}=\frac{310}{155}$

∴ t = 2 hours

The value of t  when s = 310 , $v_{1}$ = 75 , $v_{2}$ = 80 is 2 hours

Learn more:

You can learn more about distance, speed and time in brainly.com/question/1748290

#LearnwithBrainly