You skate at a rate of 12 feet per second. Your friend skates at a rate of 10 feet per seconds and has a head start of 20 feet. A. How long will it take you to catch Your friend

Correct answer: t = 10 seconds

Step-by-step explanation:

Given:

V₁ = 12 ft/s, V₂ = 10 ft/s initial distance d = 20 ft

To the moment he catches his friend the first skater will have crossed the distance d₁ and the second d₂.

d₁ = d + d₂

d₁ = V₁ · t

d₂ = V₂ · t

when we substitute this into the initial formula we get:

V₁ · t = d + V₂ · t ⇒ d = V₁ · t - V₂ · t ⇒ d = t (V₁ - V₂) ⇒ t = d / (V₁ - V₂)

t = d / (V₁ - V₂) = 20 / (12 - 10) = 20 / 2 = 10 seconds

t = 10 seconds

God is with you!