How do I translate this distance/rate/time problem into a linear system?
I'm totally lost, please help!! Toledo and Cincinnati are 200 mi apart. A car leaves Toledo traveling toward Cincinnati, and another car leaves Cincinnati at the same, traveling toward Toledo . The car leaving Toledo averages 15 mph faster than the other, and they meet after 1 hr and 36 min. What are the rates of the cars?
Mathematics - 2 Answers
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1 :
Hi Anonymous let the speed of the slower car be S, then the speed of the other car = S+15 Relative speed = sum of the speeds as the two cars are moving in opposite directons. RS = S+S+15 Now time to meet = Distance / Relative speed t = d/RS 1.6 = 200/2S+15 3.2S = 200 - 24 S = 176/3.2 = 55 mph S+15 = 55+15 = 70 So rates of the cars are 55mph and 70mph Shy
2 :
Total distance = 200mi let us say Car-A travels from Cincinnati at x miles per hour So car B travels at x+15 miles per hour from Toledo. After 1 hr 36 minutes or 1.6 hour, Car A must have covered a distance of 1.6 x miles. (Distance = average velocity X time.) After 1.6 hour, car B must have traveled a distance of 1.6 (x+15) miles Since they meet after 1.6 hour, total distance traveled 1.6 x + 1.6x+1.6 X 15 ) = 200 miles or 3.2x +24 = 200 3.2x = 200 -24 = 176 x = 176 /3.2 = 55 car A traveled at 55 miles per hour car B traveled at 55+15 = 70 miles per hour By the way, did they collide?... :)
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