On the 42-km go-cart course at Sportsworld, Arshia drives 0.4 km/h faster than Sarah, but she has engine trouble part way around the course and has to stop to get the go-cart fixed. This stop costs Arshia one-half hour, and so she arrives 15 minutes after Sarah at the end of the course. How fast did ech girl drive and how long did each girl take to finish the course? Answer to one decimal place.
Let S be Sarah's speed, Let A be Arshia's speed.
$$0.4 +S = {42 \over 0.25 + s}$$
This is all I can think of. In addition, this equation doesn't turn out to be correct...
How do I set up the equations?
We are told that if Arshia had not stopped, she would have won by $\frac 14$ hour, so we are given $$A=S+0.4\\\frac{42}A=\frac {42}S-\frac 14$$ Two equations, two unknowns.