2 trucks are traveling in the same direction, 1 going twice as fast as the other. At the end of 6 hours they are 204 miles apart. How fast is each travelling?

Question

? mph and ? mph

Answer 1

Hello Marvin.

 

Recall the equation d=rt

Distance = rate x time

 

r₁ = speed of the first truck

r₂ = speed of the 2nd truck

r₁ = 2r₂

t₁ = t₂ = 6 hours

d₁ = distance of 1st truck

d₂ = distance of 2nd truck

d₁ = d₂ + 204

 

d₁ = r₁t₁ = 6r₁

d₂ = r₂t₂ = 6r₂

 

Given the relationships we have between r₁ & r₁ and d₁ & d_{2, we can make the following substitutions}

Working with the d₁ equation

d₂+204 = 6r₁

d₂ + 204 = 6(2r₂)    New d₁ equation

The original d2 equation is

d₂ = 6r₂

 

If we subtract the original d₂ equation from the new d₁ equation, we will eliminate the d₂ term

204 = 6r₂

r₂ = 34 mph

Since r₁ = 2r₂

r₁ = 68 mph