anonymous
  • anonymous
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?
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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\[v=\frac{160}{4}miles/hr=40miles/hr\]

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