Two planes leave simultaneously from Chicago's O'Hare Airport, one flying due north and the other due east (see figure). The northbound plane is flying 50 miles per hour faster than the eastbound plane. After 3 hours the planes are 2840 miles apart. Find the speed of each plane in mi/h for northbound plane and eastbound plane (eastbound and northbound should be calculated seperated). (Round your answers to the nearest whole number.)

Question

Two planes leave simultaneously from Chicago's O'Hare Airport, one flying due north and the other due east (see figure). The northbound plane is flying 50 miles per hour faster than the eastbound plane. After 3 hours the planes are 2840 miles apart. Find the speed of each plane in mi/h for northbound plane and eastbound plane (eastbound and northbound should be calculated seperated). (Round your answers to the nearest whole number.)

the answer i got for:
eastbound plane: 643.93
northbound plane: -693.93
but when i submit it, the eastbound plane is correct but the northbound plane is wrong

Answer 1

Those would be the two roots you got when you solved the quadratic equation.

But remember x is the speed of the slower eastbound plane, so these are two possible values for just that one. You omit the negative answer as it is impossible for speed.
So we have x = 643.93 mi/h
Now, the faster northbound plane goes 50 mi/h faster than that, so its speed is 643.93 + 50 = 693.93 mi/h.

Answer 2

To find the speed of each plane, let's set up a system of equations.

Let's assume the speed of the eastbound plane is x mph. Then the speed of the northbound plane would be x + 50 mph (as it is 50 mph faster).

To find the distance traveled by each plane after 3 hours, we can use the formula distance = speed × time.

For the eastbound plane:
Distance = x mph × 3 hours = 3x miles

For the northbound plane:
Distance = (x + 50) mph × 3 hours = 3(x + 50) miles

Given that the total distance between the planes after 3 hours is 2840 miles, we can set up the following equation:

Distance eastbound plane + Distance northbound plane = Total distance
3x + 3(x + 50) = 2840

Expanding and simplifying the equation gives us:
3x + 3x + 150 = 2840
6x + 150 = 2840
6x = 2680
x = 446.67

So the speed of the eastbound plane is approximately 446.67 mph.

To find the speed of the northbound plane, we substitute this value back into the equation:
Speed northbound plane = x + 50 = 446.67 + 50 = 496.67

Therefore, the speed of the northbound plane is approximately 496.67 mph.

Rounding to the nearest whole number, the speeds are:
Eastbound plane: 447 mph
Northbound plane: 497 mph