Word problem.

Question

A train eaves a station and travels north at a speed of 50 mph. Five house later, a second train leaves on a parallel track and travels north at 175 mps. How far from the station will they meet?

Answer 1

distance=rate*time

d=rt

d=50t

d=175(t-5)

50t=175(t-5)

50t=175t-875

50t-175t=-875

-125t=-875

125t=875

t=875/125

t=7 hours

d=50*7

d=350 miles from the station

Answer 2

Let x₁ = position of the first train.

      x₂ = position of the second train.

 

Since the second train starts 5 hours later, t₁ = t₂ +5 for the relation for the times the trains travel.

 

x₁ = v₁t₁=v₁(t₂+5)=50(t₂+5)

x₂ = v₂t₂=175t₂

 

When the trains meet, x₁ = x₂.

 

50(t₂+5) = 175t₂

 

50t₂+250 = 175t₂

 

250 = 125t₂

 

t₂ = 2 hrs

 

The distance from the station would be 175*2 = 350 miles.