Question 188625
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Driver 1 distance travelled: *[tex \Large d_1]


Driver 2 distance travelled: *[tex \Large d_2]


Driver 1 rate: *[tex \Large r_1]


Driver 2 rate: *[tex \Large r_2]


Driver 1 time = Driver 2 time = 4 hours.


What we are given:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  d_1 + d_2 = 420 \ \ \Rightarrow\ \ d_2 = 420 - d_1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  r_2 = r_1 + 15]


Driver 1's trip:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  d_1 = 4r_1]


Driver 2's trip:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  d_2 = 4r_2]


Substitute from what we know:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  420 - d_1 = 4(r_1 + 15)]


Solve for *[tex \Large d_1]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  d_1 = 360 - 4r_1]


Now that we have two ways to express the value of *[tex \Large d_1], set them equal:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  4r_1 = 360 - 4r_1]


Just solve for *[tex \Large r_1], then add 15 to get *[tex \Large r_2]


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