Question

Ted and Jason are going to race their dirt bikes. Since Ted is younger, Jason is going to give him a 10 mile head start. Ted travels at 10 mph and Jason travels at 20 mph.

Write linear equations to represent each boy during the race.

Prepare a graph representing the race. Put the time in hours on the x-axis and the distance in miles on the y-axis.

At what time will Jason catch up with Ted?

How far will they have traveled when they meet?

Answer 1

With a head start of 10 miles, Ted's line starts at 10 when time is zero, or the point (0,10).  For every hour that passes, Ted's distance increases by 10 miles.  This rate of change is the slope of his line ( m = 10).
Ted's equation:  y = 10x + 10

Jason's line starts at zero since he did not get a head start, or at the point (0,0).  For every hour that passes, Jason's distance increases by 20 miles.  This rate of change is the slope of his line ( m = 20). 
Jason's equation:  y = 20x + 0

Jason will catch up with Ted when the two lines intersect or after one hour.

They will have traveled 20 miles when they meet.