1 )A race car is one lap behind the lead race car when the lead car has 49 laps to go in a race. If the speed of the lead car is 69.7m/s,what must...

The car is one lap behind the leading
car.

The lead car has 49 laps
remaining.

Therefore the second car has 49 + 1 = 50 laps
remaining.

For the lead and the second car to complete the
race at the same time, the relative speed of the two cars be such
that:

(Speed of lead car)/(Laps remaining for lead car) =
(Speed of second car)/(Laps remaining for second
car)

Substituting values of laps remaining and speed of
lead car in above equation:

(69.7/49) = (Speed of second
car)/50

==> Speed of second car = 50*(69.7/49) =
71.12245 m/s

Answer:

Required
speed of second car = 71.12245 m/s

(Please note that to
solve this problem, it is not necessary to know the length of each
lap.)