Taylor Swift leaves Philadelphia for a concert in Dallas. Kellie Pickler leaves at the same time, but in a different tour bus. After 2 hours, Taylor's bus has traveled 50% further than Kellie's bus. If Taylor's bus is going 30mph faster than kellies's bus, how fast is each bus going?
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To find the speed of each bus, we can set up a system of equations based on the given information.
Let's assume that Kellie Pickler's bus is traveling at a speed of x mph.
Since Taylor Swift's bus is going 30mph faster than Kellie's bus, we can say that Taylor's bus is traveling at (x + 30) mph.
Now, according to the information given, after 2 hours of travel, Taylor's bus has traveled 50% further than Kellie's bus. This means Taylor's bus has covered 1.5 times the distance traveled by Kellie's bus.
Let's use the equation: Distance = Speed × Time
For Taylor's bus:
Distance = (x + 30) mph × 2 hours
For Kellie's bus:
Distance = x mph × 2 hours
Since Taylor's bus has traveled 50% further, we can set up the equation:
(x + 30) mph × 2 hours = 1.5(x mph × 2 hours)
Simplifying the equation:
2(x + 30) = 1.5(2x)
2x + 60 = 3x
Subtracting 2x from both sides:
60 = x
Therefore, Kellie Pickler's bus is traveling at a speed of 60 mph.
Since Taylor's bus is going 30 mph faster, we can find its speed:
Taylor's bus = 60 mph + 30 mph = 90 mph
Hence, Kellie Pickler's bus is traveling at 60 mph, and Taylor Swift's bus is traveling at 90 mph.