Pa is driving at a speed of 30 miles per hour. One hour later Ma drives the same way at a constant speed. After driving 4 hours Ma had passed Pa and was 10 miles ahead of him. How fast was Ms driving?

Question

Pa is driving at a speed of 30 miles per hour.  One hour later Ma drives the same way at a constant speed.  After driving 4 hours Ma had passed Pa and was 10 miles ahead of him.  How fast was Ms driving?

anonymous · Answer

In the 4 hours that Ma travels, she moves a distance$$d_{Ma}=4 \times v$$where v is her speed. At the end of the 4 hours in which Ma drives, Pa has been driving for 5 (she starts out an hour later than him).  So Pa has traveled in that time,$$d_{Pa}=5hr \times 30miles/hr=150miles$$
We're told also that at this time, Ma is 10 miles ahead of Pa, so Ma's distance equals Pa's distance + 10 miles:$$d_{Ma}=d_{Pa}+10miles$$That is,$$4v=160miles$$So Ma's speed must be$$v=\frac{160}{4}miles/hr=40miles/hr$$