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when will the cars meet

  boston is 295 miles from new york city along a certain route. A car starts from Boston at 1:00pm and travels along this route toward new york city at a steady rate of 50 miles per hour. Another car starts from new york at 1:30pm and travels along this route toward boston at a steady rate of 40 miles per hour. at what time do the cars pass each other?
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3 Answers

Hey Sammi -- a half-hour headstart at 50mph removes 25mi ... 270mi left at 1:30pm ...
270mi-gap closes with combined speed of 90mph in 3hr ==> cars meet at 4:30pm :) 
Hi Sammi;
We know that the two cars combined will have traveled 295 miles at the time they pass each other.
We also know that both cars left in the pm.  Please always watch for that very carefully--a very easy oversight.
 
Distance=(rate)(time)+(rate)(time)
295 miles=(50 miles/hour)(x hours)+(40 miles/hour)[(x-0.50) hours]
Please note the fact that I indicated the time of (x-0.50) hours, not minutes.
Before we make any calculations, we must be certain that the units are align.
Let's cancel the hours which are both the numerators and denominators on the right side of the equation...
295 miles=(50 miles/hour)(x hours)+(40 miles/hour)[(x-0.50) hours]
295 miles=(50 miles)(x)+(40 miles)(x-0.50)
Let's cancel the miles...
295 miles=(50 miles)(x)+(40 miles)(x-0.50)
295=50x+[(x-0.50)40]
295=50x+40x-20
295=90x-20
Let's add 20 to both sides as we proceed to isolate x...
20+295=90x-20+20
315=90x
Let's divide both sides by 90...
315/90=(90x)/90
3.5=x
 
At 3.5 hours from the departure time of the first car, these will pass.
The first car departed at 1 pm.
4:30 pm

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