Expert: Scott A Wilson - 12/2/2009

Question
if john doe of france won the first tour de france bicycle road race in 1903. In 2005, american lone doug won his seventh consecutive tour de france. Doug's average speed in 2005 was 10 mph faster than John Doe's in 1903. in the time it took john doe to ride 80 miles, Doug could have ridden 130 miles. Find each cyclist average speed

Answer
John raced in 1903 and Doug raced in 2005.
Let John's average speed be A.  This makes Doug's average speed into A+10.

Since distance D = speed S * time T, let's set up two equations.
80 = At, where t is not known.  130 = (A+10)t, where t is the same.
This means t = 80/A and t = 130/(10+A) for the same t.
This says that 80/A = 130/(A+10).
Cross multiplying gives 80(A+10) = 130A.
Multiplying out the left side gives 80A + 800 = 130A.
Subracting 80A from both sides gives 800 = 50A.

Dividing both sides by 50 gives 16 = A, which is John's speed.
Adding 10 gives 26, which is Doug's speed.