In a flight of 600 km, an aircraft was slowed down due to bad weather.Its average speed for the trip was reduced ..............

Question

In a flight of 600 km, an aircraft was slowed down due to bad weather.Its average speed for the trip was reduced by 200 km/h and the time of flight increased by 30 minutes. Find out the duration of the flight?
Question is some says answer will be 1 hour and some 1.5 hour. Which one is the right answer?

Answer 1

In good weather:

 

(i)   600 = vt

 

In bad weather:

 

(ii)  600 = (v - 200)(t + 0.5)

 

The answer you seek is t + 0.5, so solve for t and add 0.5 hours.

 

(i) ⇒ v = 600/t

 

(ii) ⇒ 600 = (600/t - 200)(t + 0.5)

 

600t = (600 - 200t)(t + 0.5)

 

600t = 600t + 300 - 200t² - 100t

 

-200t² - 100t + 300 = 0

 

2t² + t -3 = 0 

 

Solve for t using the quadratic formula and get

 

t = 1 or -1.5

 

But time must be positive, so discard -1.5 and get

 

t = 1 hour

 

Now add to t the 0.5 hours delay and get a duration of 1.5 hours for the trip in bad weather, which is what you want; whereas 1 hour is the duration in good weather.  Test the answers.

Answer 2

Distance = rate*time  ...  d = rt

 

If r = original rate and t is original time:

Originally:  600 = rt    {equation 1}

After slow down:  600 = (r-200)(t + 0.5)    {equation 2}

 

From 600 = rt we can derive  r = 600/t

Substitute that into equation 2

 

600 = (600/t - 200)(t + 0.5)

600 = 600 + 300/t - 200t - 100

600 = 500 + 300/t - 200t

100 = 300/t - 200t

Multiply through by t

100t = 300 - 200t²

200t² + 100t - 300 = 0

Factor out 100

2t² + t - 3 = 0

2t² - 2t + 3t - 3 = 0

2t(t-1) + 3(t-1) = 0

(2t + 3)(t-1) = 0

 

Either 2t + 3 = 0   OR   t -1 = 0 

         2t = -3               t = 1

         t = -3/2

 

Since the time will not be a negative, we have t = 1 hour.

This is the time for the original flight without the slow down.

The new flight time after slowing down the rate of speed and

increasing the time of the flight is 1.5 hours