Question 1207802: In a 100-meter race,Todd crosses the finish line 5 meters ahead of Scott. To even things up, Todd suggests to Scott that they race again, this time with Todd lining up 5 meters behind the start.
(a) Assuming that Todd and Scott run at the same pace as before, does the second race end in a tie?
(b) If not, who wins?
(c) By how many meters does he win?
(d) How far back should Todd start so that the race ends in a tie?
After running the race a second time, Scott, to even things up, suggests to Todd that he (Scott) line up 5 meters in front of the start.
(e) Assuming again that they run at the same pace as in the first race, does the third race result in a tie?
(f) If not, who wins?
(g) By how many meters? (h) How far ahead should Scott start so that the race ends in a tie?
Thank you everyone for your help with word problems. Sorry for the many questions buy I truly want to increase my math skills.
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! In a 100-meter race,Todd crosses the finish line 5 meters ahead of Scott. To even things up, Todd suggests to Scott that they race again, this time with Todd lining up 5 meters behind the start.
Let Todd's time be t (s)
Todd's speed will be 100/t (m/ s)
In the same time Scott runs 95 m
Scott's speed = 95/t
Re run
Now todd runs 105 m
Scott runs 100m
Todd's time = 105/ (100/t) = 105t/100 = 1.05t (s)
Scott's time = 100/(95/t)= 100t/95 =1.0526
Assuming that Todd and Scott run at the same pace as before, does the second race end in a tie?
No
(b) If not, who wins?
Todd
(c) By how many meters does he win?
Scott's distance = 1.0526 t*95/t = 99.997 m you find the difference
(d) How far back should Todd start so that the race ends in a tie?
The time they reach should be same with different start line
If Todd runs 100+x meters and Scott 100 meters, their times should be same
t= d/r
Todd's time =Scott's time
(100+x)/(100/t) = 100/(95/t)
(100+x)t/100 = 100t/95
Divide by t
(100+x)/100 = 100/95
95(100+x) = 100*100
9500 +95x = 10000
95x = 500
x = 500/95 = 5.263 m
Todd should start about 5.2632 meters behind the start line to end in a tie.
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