A car goes uphill at the rate of 30 km an hour and downhill at the rate of 50 km an hour after 15 hours it has covered 650km. How long does it go downhill and uphill respectively?

Let the distance covered during uphill be d₁km in t₁ hr.

& the distance covered during downhill be d₂ km in t₂ hr.

According to the question, total distance = d₁ + d₂ = 650

Where, d₁ = 30t₁

d₂ = 50t₂

Therefore, 30t₁ + 50t₂ = 650 ...... (i)

Also, total time = t₁ + t₂ = 15 ...... (ii)

solving :(i) – 30(ii)

⇒ 30t₁ + 50t₂ = 650

⇒ – 30t₁ – 30t₂ = – 450

⇒ 20t₂ = 200

⇒ t₂ = 10

⇒ t₁ = 5

So, it took 5hrs to cover uphill and 10 hrs to cover downhill.