Question

Raj gets a 1.5 mile head start and runs at a rate of 4.5 miles per hour. Jacinda's progress is represented by a graph that goes through the points (1,10), (2,20), and (3,30). How long will Jacinda need to run to catch up with Raj?

Answer 1

From the given ordered pair representing Jacinda's progress, her speed is equal to 10 miles per hour. Letting x be the time it takes for Jacinda to catch up with Raj, the total distance Raj would travel is 
                            1.5 + 4.5x
and Jacinda's total distance is 10x. Mathematically,
                                1.5 + 4.5x = 10x 
The value of x from the equation is 0.27 hours. Therefore, Jacinda needs to run 2.7 miles to catch up with Raj.