I need help with this problem:
Two planes start from Los Angeles International Airport and fly in opposite directions. The second plane starts ½ hour after the first plane, but its speed is 80 kilometers per hour faster. Find the airspeed of each plane if 2 hours after the first plane departs the planes are 3200 kilometers apart.
distance slow plane=vt
distance fast plane=.5*(v+80)t +(v+80)t
3200=sum of the two distances, or
3200=v*2+.t(v+80)*2 + (v+80)*2
solve for v, then for the faster plane, its speed is v+80
Whats 1/5 (one fifth) of 200?
40 times five is 200
To solve this problem, we can use the formula Distance = Speed × Time. Let's break down the information we have:
- The first plane starts flying 2 hours before the second plane.
- The second plane starts flying 1/2 hour after the first plane.
- The speed of the second plane is 80 kilometers per hour faster than the first plane.
- After 2 hours, the planes are 3200 kilometers apart.
Let's assign some variables to the unknowns:
Let x be the airspeed of the first plane.
The airspeed of the second plane will then be x + 80 (as it is 80 kilometers per hour faster).
Now, let's calculate the distance covered by each plane:
Distance covered by the first plane = Speed of the first plane × Time
= x km/h × 2 hours
= 2x km
Distance covered by the second plane = Speed of the second plane × Time
= (x + 80) km/h × (2 - 1/2) hours
= (x + 80) km/h × 1.5 hours
= 1.5(x + 80) km
The total distance between the planes is 3200 kilometers. Therefore, we can set up the equation:
Distance covered by the first plane + Distance covered by the second plane = Total distance
2x + 1.5(x + 80) = 3200
Now, we can solve this equation to find the value of x:
2x + 1.5x + 120 = 3200
3.5x + 120 = 3200
3.5x = 3200 - 120
3.5x = 3080
x = 3080 / 3.5
x ≈ 880
So, the airspeed of the first plane is approximately 880 kilometers per hour.
To find the airspeed of the second plane, we can substitute the value of x back into one of the previous expressions:
Speed of the second plane = x + 80
= 880 + 80
= 960
Therefore, the airspeed of the second plane is 960 kilometers per hour.
In summary, the airspeed of the first plane is approximately 880 kilometers per hour, and the airspeed of the second plane is 960 kilometers per hour.