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:
a
s=250, v1 = 60 , v2 = 40

The formula for t is:
(A) s · (v1 +v2)
(B) s v1 +v2
(C) s v2 −v1
(D) v1 +v2 s
(E) (v2 −v1) ·s

Answer 1

Answer:

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

The value of t is, $2\dfrac {1}{2}$ hour

Step-by-step explanation:

The 1st train travels at $v_{1}$ mph whereas the 2nd train travels at

$v_{2}$ mph. The trains are headed towards each other. They are s miles apart. In 1 hour their distance is reduced by $(v_{1} + v_{2})$ mile

So, in t hour their distance is reduced by $(v_{1} + v_{2}) \times t$ mile.

Now if the two trains  meet after t hour of starting, then,

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

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

If s = 250 unit, $v_{1}$ = 60 unit and, $v_{2}$ = 40 unit , then,

from (1), t = (250/(60 + 40)) hour  = $2\dfrac {1}{2}$ hour ----(2)