Kim starts to walk 3 mi to school at
7:30 A.M. with a temperature of 0°F. Her brother Bryan starts at 7:50 A.M. on his bicycle, traveling 10 mph faster
than Kim. If they get to school at the same time, then how fast is each one traveling?
I have tried to answer this word problem by using the formula d=rt, and the try and figure out what is the value of r. I got a complex fraction of -30t+19/3t-1. I want to know if I am right or wrong. If I am wrong, could you walk me through the steps to sovling this word problem. Thank so much for your time, and help.
To solve this word problem, let's break it down step by step.
1. Let's first determine the time it takes for Kim to reach school. Kim starts at 7:30 A.M., and let's say it takes her t hours to reach school. Therefore, she arrives at 7:30 A.M. + t hours.
2. Bryan starts at 7:50 A.M., which means he starts 20 minutes (or 1/3 hours) later than Kim. Since they both arrive at the same time, Bryan's travel time is t - 1/3 hours.
3. Now, let's calculate the distance each of them travels. Kim travels 3 miles, so using the formula d = rt, we have d = 3 miles and t hours. Thus, Kim's speed can be determined as r = d/t = 3/t miles per hour.
4. Bryan travels 10 mph faster than Kim, so his speed can be determined as r = (3/t) + 10 miles per hour.
5. Since they both arrive at school at the same time, their travel times are equal. Therefore, we can set up the equation: t = t - 1/3.
Now, let's solve for t and find their speeds:
t = t - 1/3
1/3 = 0
We have a contradiction in the equation, so there might be an error in our setup.
The problem states that Bryan travels 10 mph faster than Kim but doesn't provide any information on their actual speeds. Let's assume the speeds are represented by x mph for Kim and (x + 10) mph for Bryan.
Using the formula d = rt for both Kim and Bryan, we can set up two equations:
Kim's equation: 3 = x * t
Bryan's equation: 3 = (x + 10) * (t - 1/3)
To solve for x and t, we can substitute Kim's equation into Bryan's equation:
3 = (x + 10) * (x * t - 1/3) [Substituting x * t from Kim's equation]
Expanding the equation, we get:
3 = (x + 10)(xt - 1/3)
3 = x^2t + 10xt - (1/3)(x + 10)
Now, let's simplify:
3 = x^2t + 10xt - (x + 10)/3
To solve this equation, we'd need more information about the values of x and t, such as a numerical value for one of the variables or additional equations. Without that specific information, we can't provide exact values for Kim and Bryan's speeds.
Unfortunately, the complex fraction you mentioned (-30t + 19) / (3t - 1) does not seem to be the correct solution to this word problem.