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After how long will Rachel's sister catch up with her?

Rachel leaves on a business trip, forgetting her laptop computer. Her sister discovers it 2 hours later, and knowing that Rachel needs it for her sales presentation and that Rachel normally travels at a speed of 55mph, decides to follow her at a rate of 75mph. after how long will Rachel's sister catch up with her?
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2 Answers

Hi Ryan;
Distance=rate x time
miles= (miles/hour)(hours)
  
 
(55 miles/hour)(2+x)hours=(75 miles/hour)(x hours)
Let's cancel units...
(55 miles/hour)(2+x)hours=(75 miles/hour)(x hours)
Let's cancel units...
(55 miles)(2+x)=(75 miles)(x)
55(2+x)=75x
110 + 55x=75x
Let's subtract 55x from both sides...
-55x+110+55x=75x-55x
110=20x
Let's divide both sides by 20...
110/20=20x/20
5.5=x
 
The sister will catch-up in 5.5 hours.
 
Let's check our work...
(55 miles/hour)(2+x)hours=(75 miles/hour)(x hours)
(55 miles/hour)(2 + 5.5)hours=(75 miles/hour)(5.5 hours)
(55 miles/hour)(7.5 hours)=(75 miles/hour)(5.5 hours)
412.5 miles=412.5 miles
 
It will be a long trip.