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?

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

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# 2 Answers

110+55h=75h

110=20h

h=5.5hours

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.