66) A plane left 40 minutes late due to bad weatherand in order to rea

1.	66) A plane left 40 minutes late due to bad weatherand in order to reach its destination, 1600km awayin time, it had to increase its speed by 400km/hrfrom its usual speed. Find the usual speed of theplane.
Answer» Distance = 1600 km Let the usual speed be = x km/h now, we know that speed = distance /timetime = distance / speed Usual time = 1600/x Now, due to bad weather the speed is increased b 400 km/ hr which means new speed = 1600/x+400 Now it's given that the plain left 40 minutes late which means new time = 1600/(x+400) + 2/3 (40/60 = 2/3 hours) 1600/x = 1600/(x+400) + 2/3 1600/x-1600/(x+400) = 2/3 1600(x+400)-1600x/x(x+400) = 2/3 1600x + 640000-1600x/x²+400x = 2/3 640000 = 2/3(x²+400x) 640000 * 3/2 = x²+400x 960000 = x² +400x 0 = x²+400x-960000 0 = x² +1200x-800x-960000 0 = x( x+ 1200) - 800(x+1200) 0= (x+1200)(x-800) x= -1200 or x= 800 Speed cannot be negative∴ usual speed = 800 km/h

66) A plane left 40 minutes late due to bad weatherand in order to reach its destination, 1600km awayin time, it had to increase its speed by 400km/hrfrom its usual speed. Find the usual speed of theplane.

Answer»

Distance = 1600 km

Let the usual speed be = x km/h

now, we know that

speed = distance /timetime = distance / speed

Usual time = 1600/x

Now, due to bad weather the speed is increased b 400 km/ hr

which means new speed = 1600/x+400

Now it's given that the plain left 40 minutes late

which means new time = 1600/(x+400) + 2/3 (40/60 = 2/3 hours)

1600/x = 1600/(x+400) + 2/3

1600/x-1600/(x+400) = 2/3

1600(x+400)-1600x/x(x+400) = 2/3

1600x + 640000-1600x/x²+400x = 2/3

640000 = 2/3(x²+400x)

640000 * 3/2 = x²+400x

960000 = x² +400x

0 = x²+400x-960000

0 = x² +1200x-800x-960000

0 = x( x+ 1200) - 800(x+1200)

0= (x+1200)(x-800)

x= -1200 or x= 800

Speed cannot be negative∴ usual speed = 800 km/h