SOLUTION: Lewiston and Vernonville are 128 miles apart. A car leaves Lewiston traveling towards​ Vernonville, and another car leaves Vernonville at the same​ time, traveling towards Lewi

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Question 1158413: Lewiston and Vernonville are 128 miles apart. A car leaves Lewiston traveling towards​ Vernonville, and another car leaves Vernonville at the same​ time, traveling towards Lewiston. The car leaving Lewiston averages 10 miles per hour more than the​ other, and they meet after 1 hour and 36 minutes. What are the average speeds of the​ cars?
Found 3 solutions by Shin123, josgarithmetic, solver91311:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
The car leaving Vernonville averages x mph, and the other car averages (x+10) mph. After 1.6 hours, they meet. The car leaving Vernonville traveled 1.6x miles and the other car traveled 1.6x+16. The sum of these values are 128. 1.6x%2B%281.6x%2B16%29=128. 3.2x%2B16=128. 3.2x=112. x=112%2F3.2=35. x%2B10=45. The car leaving Vernonville averages 35 mph, and the other car averages 45 mph.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
r%2A%281%2636%2F60%29%2B%28r%2B10%29%281%2636%2F60%29=128


%281%263%2F5%29r%2B%281%263%2F5%29%28r%2B10%29=128

8r%2B8%28r%2B10%29=640

8r%2B8r%2B80=640
16r=640-80
16r=560

highlight%28r=35%29---------------the car from Vernonville
45---------------------speed of car from Lewiston

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Since the cars are traveling toward each other, their combined rate of speed is the sum of their rates of speed. Since the entire trip of 128 miles was completed in 1 hour and 36 minutes, which is to say 1.6 hours, the combined rate of speed must be:



Let represent the speed of the slower car, then must be the speed of the faster car, and the sum of these two quantities must be the combined speed, namely . In short:



Solve for and then calculate


John

My calculator said it, I believe it, that settles it