Question

A plan traveled for a total of 2,773 miles over the course of 8 hours. Heading south, the plan traveled at an average speed of 344 miles per hour and heading west. It traveled at an average speed of 351 miles per hour. For how many hours was the plane heading south?

Answer 1

5 hours

Explanation:

Let s and w represent hours spent traveling south and west, respectively. The problem statement tells us ...

s + w = 8 . . . . . . total trip time

344s + 351w = 2773 . . . . total mileage (using d = s·t)

By Cramer's rule, we can find the value of s as ...

s = (1(2773) -351(8))/(1(344) -351(1)) = -35/-7 = 5

The plane was heading south for 5 hours.

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Comment on Cramer's rule

For the equations ...

ax +by = c

dx +ey = f

The solution for x can be found to be ...

x = (bf-ec)/(bd-ea)

Similarly, the solution for y is ...

y = (cd-fa)/(bd-ea)