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

• 80km/h and 60km/h

Step-by-step 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