Bad weather

An aircraft was slowed down during a 600 km flight due to bad weather. Its average speed was reduced by 200 km/hr from its usual speed, and the flight time increased by 30 minutes. Find the scheduled duration of the flight.

Correct answer:

t =  1 h

Step-by-step explanation:

s=600 km Δ=200 km/h T=30 min h=30:60  h=0.5 h  v2 = v1  Δ  t2 = t + T  t = s/v1 t2 = s/v2= t+T = s/v1 + T  s/v2 = s/v1+T s/(v1Δ) = s/v1+T  s v1 = s (v1Δ)+T (v1Δ) v1  s x=s (xΔ)+T (xΔ) x  600 x=600 (x200)+0.5 (x200) x 0.5x2+100x+120000=0 0.5x2100x120000=0  a=0.5;b=100;c=120000 D=b24ac=100240.5(120000)=250000 D>0  x1,2=2ab±D=1100±250000=100±5001 x1,2=100±500 x1=600 x2=400 v>0 v1=x1=600 km/h v2=v1Δ=600200=400 km/h  t=s/v1=600/600=1 h   Verifying Solution:   t2=s/v2=600/400=23=1.5 h

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