Expert: Chanda Walker - 1/16/2009

Question
QUESTION: Please Dont just give me the answer, show me how to get the answer. Show me the work. Thank you!

Runner A crosses the starting line of a marathon and runns at an average pace of 5.6 mph. Half an hour later, Runner B crosses the starting line and runs at an average rate of 6.4 mph. If the length of the marathon is 26.2 miles, which runner will finish ahead of the other? Explain.
A/. Runner B; Runner B will catch up to runner A 4 hours after Runner A Crosses the starting line.
B/. Runner B; Runner B will pass Runner A and finish more than half an hour ahead of Runner A.
C/. Runner B; Runner B will catch up to Runner A 3.5 hours after runner A crosses the starting line.
D/. Runner A; Runner B will not be able to catch up to Runner A in time.

ANSWER: All we need to know is when the runners will be at the same place and we need to make sure that the race isn't over before that time.

The speed of Runner A multiplied by the time (unknown) will equal the speed of Runner B multiplied by the time minus half an hour.

5.6 * t = 6.4 *(t - .5)

.5 = (6.4 - 5.6)t
6.4*.5 = (0.8) t
t = 4.

Let's just be sure the race wasn't won before the runner B caught up.  Specifically before 4 hours time.

5.6*4 = 22.4 miles.

Nope, a marathon is approximately 26 miles so it is clear that only answer A is correct.

Answer A is your answer.


---------- FOLLOW-UP ----------

QUESTION: Please, i really need this problem done by at the latest in a few hours. It is 10:00 pm eastern time for me, and i am having a test with this question on it:
A class writes an equation: n+n+1+n+2=87
To solve this:The sum of 3 consecutive odd intergers is 87. Find the 3 intergers. What error did they make?

Answer
Ah well that equation would give you the sum of three consecutive integers NOT consecutive ODD integers.  Let's change the equation.

n + n+2 + n+4 = 87

odd integers are 2 apart not 1 apart.

Solving this we get

3n + 6 = 87
3n = 81
n=27

Since the sum equaled an odd number (87) there is no way that you could get anything but an odd solution.

Your integers are 27, 29, 31

Does that make sense?  Let me know if I can help further!