Question

Two cars left the city for a suburb, 480 km away, at the same time. The speed of one of the cars was 20 km/hour greater than the speed of the other, and that is why it arrived at the suburb 2 hour earlier than the other car. Find the speeds of both cars.

Answer 1

Answer:

• 80km/h and 60km/h

Explanation:

1. Data:

i) Distance traveled by the cars:

• d = 780 km

ii) Speed of the cars:

• v₁ and v₂

• v₁ = v₂ + 20 km/h

iii) Time to arrive at the suburb:

• t₂ - t₁ = 2 hour ⇒ t₂ = t₁ + 2

2. Equations:

• speed = distance / time

        time  = distance / speed

• t₂ = 480 / v₂
• t₁ = 480 / v₁ = 480 / (v₂ + 20)

               t₂        -       t₁                =  2 hour

               ↓                 ↓                    ↓

           480/v₂    -  480/ (v₂ + 20) =  2

             

3. Solve the equation

     480(v₂ + 20) - 480(v₂) =  2 × (v₂ + 20) (v₂)

     240(v₂ + 20) - 240(v₂) =  (v₂ + 20) (v₂)

     240v₂ + 4800 - 240v₂ =  (v₂)²  + 20v₂

      (v₂)²  + 20v₂ - 4800 = 0

      (v₂ + 80) (v₂ - 60) = 0

      v₂ = - 80

      v₂ = 60

Only the positive solution has physical meaning:

• v₂ = 60km/h                                      ← answer

• v₁ = 60km/h + 20km/h = 80km/h     ← answer