SOLUTION: Two cars start out at the same spot. One car starts to drive north at 40 mph and 3 hours later the second car starts driving to the east at 60 mph. How long after the first car sta

Question 1184012: Two cars start out at the same spot. One car starts to drive north at 40 mph and 3 hours later the second car starts driving to the east at 60 mph. How long after the first car starts driving does it take for the two cars to be 500 miles apart?
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

The point marked is where the northbound car was located when the eastbound car started. (40∙3 or 120 miles north of where it started). Solve by the quadratic formula and get 5.871020759 hours from the time the second car started, which was 3 hours more than that for the time after the first car started, or 8.871020759 hours. Edwin

Answer by ikleyn(52772) (Show Source): You can put this solution on YOUR website!
.
Two cars start out at the same spot. One car starts to drive north at 40 mph.
3 hours later the second car starts driving to the east at 60 mph.
How long after the first car starts driving does it take for the two cars to be 500 miles apart?
~~~~~~~~~~~~~~~~~

Let "t" be the time chronometered after the first car starts. First car traveled t hours; second car traveled (t-3) hours (assuming t >= 3). The distance between the cars is then = 500. It is the equation to solve in order for to find "t". Square both side (40*t)^2 + (60*(t-3))^2 = 500^2 1600t^2 + 3600t^2 - 3600*6t + 9*3600 = 250000 5200t^2 - 21600t + 32400 = 250000 5200t^2 - 21600t - 217600 = 0. 520t^2 - 2160t - 21760 = 0 Use the quadratic formula. The positive root is approximately 8.87 hours. ANSWER. 8.87 hours after the first car started. CHECK. = 500 miles (total distance). ! Correct !

Solved.

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