I'm just a little confused on how to set up the problem about how far a faster car has to travel to beat the slower car by x minutes. Anybody know how to set it up?
Tough question. You know that v=x/t so if you do some algebra you know that t=x/v. So for the slower car t1=x1/v1.
For the faster car t2=x2/v2 or you can write t1-19=x2/v2 (that's if the car is 19 minutes faster than the slower car). And since you want the distances for both cars to be the same you can make x2 the same as x1 so you can write the equation as t1-19=x1/v2. If you solve the last equation for t1 you get t1=19 + x1/v2.
Now you have t1= two different equations. If you put those two equations equal to each other because t1=t1: x1/v1=19+x1/v2. Remember that the number 19 is just the number of minutes different for your problem.
That's a messy equation but you should be able to solve for x1 (algebra, algebra, algebra!).
Sorry, but it's not really helping me. Would that mean that x1 = (19(v1)(v2))/(v2-v1)? Cause that is what I think the equation would be after it's all put to one side.
3 comments:
Tough question.
You know that v=x/t so if you do some algebra you know that t=x/v. So for the slower car t1=x1/v1.
For the faster car t2=x2/v2 or you can write t1-19=x2/v2 (that's if the car is 19 minutes faster than the slower car). And since you want the distances for both cars to be the same you can make x2 the same as x1 so you can write the equation as t1-19=x1/v2. If you solve the last equation for t1 you get t1=19 + x1/v2.
Now you have t1= two different equations. If you put those two equations equal to each other because t1=t1: x1/v1=19+x1/v2. Remember that the number 19 is just the number of minutes different for your problem.
That's a messy equation but you should be able to solve for x1 (algebra, algebra, algebra!).
Hope that helps. Good luck.
Sorry, but it's not really helping me. Would that mean that x1 = (19(v1)(v2))/(v2-v1)? Cause that is what I think the equation would be after it's all put to one side.
Actually, never mind. I just got it. Thanks so much! I just forgot to get a better common denominator. See ya tomorrow!
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