Quadratic Functions solve problem: Applications involving Quadratic equations

Question

During the first part of a canoe trip, Ben covered 60km at a certain speed. He then traveled 24 km at a speed that was 4km/h slower. If the total time for the trip was 8 hr, what was the speed on each part of the trip.

Answer 1

t = t₁ + t₂ = d₁/v₁ + d₂/v₂

 

where we have used the basic distance = speed x time formula.

 

 

v₂ = v₁ - 4

 

8 = 60/v₁ + 24/(v₁ - 4)

 

After clearing fractions,

 

8v₁(v₁ - 4) = 60(v₁ - 4) + 24v₁

 

8v₁² - 32v₁ = 84v₁ - 240

 

8v₁² - 116v₁ + 240 = 0

 

v₁² - 14.5v₁ + 30 = 0

 

v₁ = 14.5/2 + ½√(14.5² - 4(30)) = 7.25 ± 4.75 = 12 or 2.5

 

Since the slower speed can't be negative, v₁ = 12 km/hr and v₂ = 8 km/hr.