Problema Solution
Tom and Silas ran a 100 meter race. When Tom crossed the finish line, Silas had run only 95 meters. Then they ran a second race, with Tom starting 10 meters behind the starting line. Assuming that both runners at the same pace as in the first race, who won the second race?
Answer provided by our tutors
Let
s = Silas's rate
t = Tom's rate
We will use the formula:
avg.speed = distance/time
time = distance/avg.rate
Tom and Silas ran a 100 meter race. When Tom crossed the finish line, Silas had run only 95 meters:
100/t = 95/s
t = 100s/95
t = 20s/19
The second race Tom is running distance of 110 m. Tom's time in this case is: 110/t
We need to compare 110/t and 100/s.
Plug t = 20s/19 into 110/t:
110/(20s/19) = 110*19/20s = 104.5/s
Tom's time running 110 m is: 104.5/s while Silas's time is 100/s. Since Silas's time is shorter that Tom's time, that is: 100/s < 104.5/s we conclude that the second race was won by Silas.