I Need the Answers to these Problems: Two cars start out at the same spot....

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spaceshowfeature1

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I need the answers to the following problems to 4 decimal points.


  • Two cars start out at the same spot. One car starts to drive north at 18 mph 5 hours before the second car starts driving to the east at 32 mph. How long after the first car starts driving does it take for the two cars to be 350 miles apart?


  • Two cars start out at the same point and at the same time one starts driving north while the other starts driving east at a speed that is 4 mph faster than the car driving north. Twelve hours after the cars start driving they are 600 miles apart. What was the speed of each car?
Thanks!

Also, where could I find problems similar to these? They are Pythagorean Theorem Distance, Rate, and Time Problems.
 
spaceshowfeature1 said:
I need the answers to the following problems to 4 decimal points.
  • Two cars start out at the same spot. One car starts to drive north at 18 mph 5 hours before the second car starts driving to the east at 32 mph. How long after the first car starts driving does it take for the two cars to be 350 miles apart?
Click to expand...
x hours (x> 5) the first car will have gone 18x miles. The second car, which will have been driving for x- 5 hours, will have gone 32(x- 5) miles. The Pythagorean theorem says that, if the two legs or a right triangle are "a" and "b" then the length of the hypotenuse, c, is given by \(\displaystyle c^2= a^2+ b^2\). Here that will be \(\displaystyle (18x)^2+ (32(x- 5))^2= 350^2\). Solve that quadratic equation for x.

  • Two cars start out at the same point and at the same time one starts driving north while the other starts driving east at a speed that is 4 mph faster than the car driving north. Twelve hours after the cars start driving they are 600 miles apart. What was the speed of each car?
Click to expand...
Let x be the speed of the first car in miles per hour. After 12 hours it will have gone 12x miles. The other car, driving east, has speed x+ 4. After 12 hours it will have gone 12(x+ 4) miles. Again by the Pythagorean theorem, \(\displaystyle (12x)^2+ (12(x+ 4)^2= 600^2\). Solve that equation for x.

Thanks!

Also, where could I find problems similar to these? They are Pythagorean Theorem Distance, Rate, and Time Problems.
Click to expand...
 
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HallsofIvy said:
x hours (x> 5) the first car will have gone 18x miles. The second car, which will have been driving for x- 5 hours, will have gone 32(x- 5) miles. The Pythagorean theorem says that, if the two legs or a right triangle are "a" and "b" then the length of the hypotenuse, c, is given by \(\displaystyle c^2= a^2+ b^2\). Here that will be \(\displaystyle (18x)^2+ (32(x- 5))^2= 350^2\). Solve that quadratic equation for x.


Let x be the speed of the first car in miles per hour. After 12 hours it will have gone 12x miles. The other car, driving east, has speed x+ 4. After 12 hours it will have gone 12(x+ 4) miles. Again by the Pythagorean theorem, \(\displaystyle (12x)^2+ (12(x+ 4)^2= 600^2\). Solve that equation for x.
Click to expand...

how do you know that the car was traveling at x-5 hours. I would think that it would be x+5, because the car has already traveled for 5 miles. Now that I have that problem wrong, I’m out of problems. I need more problems like these, or else I’m not going to be able to be Good at them. For the love of God, could you help me find some more problems like these? I’m now upset because I spent 45 minutes on that first problem, and it was one simple error due to SIMANTICS. The north car started traveling 5 hours before the second one, so that makes me assume that it would be x+5. X is the hours on the other car, then I add in the five hours the north car has already been traveling and get x+5.

Second of all, the first problem (not shown here) said that in their problem a car traveled 3 hours after another on started, while this problem talks about a car traveling before another car, which got me thinking that the first car was traveling at x+5 hours.

Overall, I need more practice problems so I can become successful, because I just spent 45 minutes of my time with a wrong answer, and I feel like an idiot.
 
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spaceshowfeature1 said:
how do you know that the car was traveling at x-5 hours. I would think that it would be x+5, because the car has already traveled for 5 miles.
Click to expand...
No, perhaps you are misreading. The problem said that the first car started "5 hours before the second", not 5 miles.

Now, suppose that first car started at 6:00 A.M.. The second car started 5 hours later, at 11:00. At, say, 3:00 P.M. the first car will have been traveling for x= 9 hours (6 hours until noon then 3 more hours). The second car will have traveled 4 hours: x- 5= 9- 5.

Now that I have that problem wrong, I’m out of problems. I need more problems like these, or else I’m not going to be able to be Good at them. For the love of God, could you help me find some more problems like these? I’m now upset because I spent 45 minutes on that first problem, and it was one simple error due to SIMANTICS. The north car started traveling 5 hours before the second one, so that makes me assume that it would be x+5. X is the hours on the other car, then I add in the five hours the north car has already been traveling and get x+5.

Second of all, the first problem (not shown here) said that in their problem a car traveled 3 hours after another on started, while this problem talks about a car traveling before another car, which got me thinking that the first car was traveling at x+5 hours.

Overall, I need more practice problems so I can become successful, because I just spent 45 minutes of my time with a wrong answer, and I feel like an idiot.
Click to expand...
 
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