Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 78 kmh faster than the other. If the two planes are 6400 kilometers apart after 4 hours, what is the rate of each plane?Note that the ALEKS graphing calculator can be used to make computations easier.Rate of the faster plane: kmhRate of the slower plane: kmh
Question
Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 78 kmh faster than the other. If the two planes are 6400 kilometers apart after 4 hours, what is the rate of each plane?Note that the ALEKS graphing calculator can be used to make computations easier.Rate of the faster plane: kmhRate of the slower plane: kmh
Solution
Let's denote the speed of the slower plane as x (in km/h). Therefore, the speed of the faster plane is x + 78 km/h.
Since they are moving in opposite directions, their speeds are added together. So, their combined speed is x + (x + 78) = 2x + 78 km/h.
They are 6400 kilometers apart after 4 hours, so their combined speed is 6400 km / 4 hours = 1600 km/h.
Setting this equal to the expression for their combined speed gives us the equation 2x + 78 = 1600.
Solving this equation for x gives us the speed of the slower plane:
2x = 1600 - 78 2x = 1522 x = 1522 / 2 x = 761 km/h
Therefore, the speed of the slower plane is 761 km/h and the speed of the faster plane is 761 km/h + 78 km/h = 839 km/h.
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