SOLUTION: two cars traveled in opposite directions from the same starting point. The rate of one car was 15km/h faster than the rate of the other car. After 2hr, the cars were 240 kn apart.

Question 82309: two cars traveled in opposite directions from the same starting point. The rate of one car was 15km/h faster than the rate of the other car. After 2hr, the cars were 240 kn apart. find each car's rate?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
distance(d)=rate(r) times time(t) or d=rt; r=d/t and t=d/r
Let r=rate of first car
Then r+15=rate of other car
Distance first car travels in 2 hours=rt=2r
Distance other car travels in 2 hours=rt=2(r+15)
Now we are told that the distance first car travels plus the distance second car travels equals 240 km. So:
2r+2(r+15)=240 get rid of parens
2r+2r+30=240 subtract 30 from both sides
2r+2r+30-30=240-30 collect like terms
4r=210 divide both sides by 4
r=52.5 km/hr----------------------------rate of first car
r+15=52.5+15=67.5 km/hr---------------------rate of other car
CK
2(52.5)+2(67.5)=240
105+135=240
240=240

Another way to look at this problem is to note that the two cars are separating at the rate of (r+r+15) km/hr . So in 2 hrs, they will have separated 2(r+r+15) km or 2r+2r+30 and that equals 240 km---same eq as before.

Hope this helps--------------------ptaylor

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