Question 216446
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First thing:  Stop typing your posts in ALL CAPS.  It is the electronic equivalent of shouting and is therefore both annoying and unacceptably rude behavior.


Use <i>distance equals rate times time</i> or *[tex \Large d\ =\ rt]


Rearrange it so that time is expressed in terms of distance and rate, thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t = \frac{d}{r}]


So, the time required for the car to travel 50 miles is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t = \frac{50}{r}]


where *[tex \Large r] is the speed of the car.


Since *[tex \Large r] is the speed of the car and the plane travels 143 mph faster than that, the speed of the plane must be *[tex \Large 143 + r]


Now you can write a statement for the time it takes the plane to travel 180 miles:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t = \frac{180}{143+r}]


But the problem says that these two times are equal, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{180}{143+r}\ =\ \frac{50}{r}]


Cross-multiply:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 180r\ =\ 50(143 + r)]


Just solve for *[tex \Large r]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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