<PRE><B>Question 250722</B>
This is an RTD problem. Here is the table
vehicle . . . . . . . rate . . . . . . . . time . . . . . . . .distance
cycle . . . . . . . . . R . . . . . . .. . . 270/R . . . . . .. 270
cycle . . . . . . . . .R + 15 . .. . . . 270/R - 3 . . . .. 270

I let R = rate. The first time is D / R = 270 / R. All times are in hours, so the second time is 
(270/R - 3) hours.
Look at the second line.
(R + 15)(270/R - 3) = 270
By FOIL, we get
270 - 3R + 4050/R - 45 = 270
multiply both sides by R. we get
270R - 3R^2 + 4050 - 45R = 270R.
Simplify to get
3R^2 + 45R - 4050 = 0
dividing by 3, we get
R^2 + 15R - 1350 = 0
factoring, we get
(R + 45)(R - 30) = 0
R = -45 or R = 30.
we can use -45, so
R = 30. The motorcycle was traveling at 30 mph.</PRE>