## anonymous 5 years ago 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?

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$v=\frac{160}{4}miles/hr=40miles/hr$