Question

if the average speed of a light plane had been 40 km/h less, the plane would have taken one hour longer to fly the 1200 km route. what was the average speed of the plane?

Answer 1

The average speed of the plane is 240 km/h

Average speed is the ratio of total distance travelled to total time taken. It is given by:

Average speed = total distance / total time

Let S represent the average speed of the plane.

S = 1200/t

When driving 40 km/h less, the total time = t + 1 hour, hence:

S - 40 = 1200 / (t + 1)

1200/t - 40 = 1200/(t+ 1)

1200 - 40t + 1200/t - 40 = 1200

- 40t + 1200/t - 40 = 0

Multiply through by t:

- 40t² + 1200 - 40t = 0

This gives t = 5 and t = -6

Since the time cannot be negative, hence the total time is 5 hours. Hence:

S = 1200/t = 1200 / 5 = 240 km/h

Hence the average speed of the plane is 240 km/h.

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Answer 2

Speed is a scalar quantity, we will ignore the negative sign.

The average speed of the plane is 240 km/h

The Parameters to work with in this question are :

Speed, Time and distance. Where

distance S = 1200 km and the formula for speed is

Speed V = distance S / Time T

The assumed equation for this assumption will be:

(V - 40) = 1200/ (T + 1 )

Cross multiply and open the bracket

(V - 40)(T + 1) = 1200 ............. Equation 1

The real equation for the real scenario will be

V = 1200/ t

Where V is the average speed of the plane.

Make t the subject of the formula

t = 1200/V

Substitute the above t in equation 1 since we are looking for V

(V - 40)(1200/V + 1) = 1200

Open the bracket

1200 + V - 48000/V - 40 = 1200

Rearrange

V - 48000/V + 1160 = 1200

V - 48000/V = 1200 - 1160

$V^{2}$ - 48000 = 40V

$V^{2}$ - 40V - 48000

The two numbers to multiply together to give -48000 and add together to give -40 are -240 and 200

$V^{2}$ - 240V + 200V - 48000

V - 240 = 0 or V + 200 = 0

V = 240 or - 200

Since the speed is a scalar quantity, we will ignore the negative sign.

Therefore, the average speed of the plane is 240 km/h

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