# Math Help - Find the speed

1. ## Find the speed

Plane A and Plane B flew in opposite directions around the Earth (40,000 km).
Plane A covered half its distance at a speed of 2,500 km/h and the other half at a speed of 1,000 km/h.
Plane B spent half its time at 2,500km/h and the other half at 1,000 km/h.
How long did it take each plane to complete the flight.

Ok so I found the time of Plane A, half the distance being 20,000 km if i'm correct.
Therefore Plane A took 28 Hours.

Problem is i have no idea how to tell how long it took Plane B. Any help please.

2. Originally Posted by Raj
Plane A and Plane B flew in opposite directions around the Earth (40,000 km).
Plane A covered half its distance at a speed of 2,500 km/h and the other half at a speed of 1,000 km/h.
Plane B spent half its time at 2,500km/h and the other half at 1,000 km/h.
How long did it take each plane to complete the flight.

Ok so I found the time of Plane A, half the distance being 20,000 km if i'm correct.
Therefore Plane A took 28 Hours.

Problem is i have no idea how to tell how long it took Plane B. Any help please.
d = vt

Plain A:
First half of trip:
d = 20000 km
v = 2500 km/h

So $t = \frac{d}{v} = \frac{20000~km}{2500~km/h} = 8~h$

Second half of trip:
d = 20000 km
v = 1000 km/h

So $t = \frac{d}{v} = \frac{20000~km}{1000~km/h} = 20~hr$

Thus t = 28 hours, as you say.

Plain B:

Let the total trip time be T.

Then
t = (1/2)T
v = 2500 km/h

$d_1 = vt = (2500~km/h) \cdot \left ( \frac{T}{2} \right ) = 1250T$

For the second half of the trip:
t = (1/2)T
v = 1000 km/h

$d_2 = vt = (1000~km/h) \cdot \left ( \frac{T}{2} \right ) = 500T$

And we know the total trip distance is d1 + d2 = 40000 km. Thus
$40000 = 1250T + 500T$

Solve for T.

-Dan