SOLUTION: gerry and rachel love to ride their bikes, and often spend weekend days riding together. Gerry is the faster rider, and on this weekend, she wanted to spend some time riding fast o

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Question 1038326: gerry and rachel love to ride their bikes, and often spend weekend days riding together. Gerry is the faster rider, and on this weekend, she wanted to spend some time riding fast on her own. and some time riding with rachel. They agreed on a route and rachel started riding at 8am at 8 miles per hour. Gerry started from the same place at 10am and rode at 10 miles per hour. At what time did gerry overtake Rachel? How far had they gone by then?
Answer by Othel(27) (Show Source):
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We have been told that Rachel's rate is 8 miles an hour, and that Gerry's rate is 10 miles an hour.
We are also told that Gerry started 2 hours later than Rachel.
We need to find when the distance that the two have traveled is equal.
We know that . And we know that the distance is the same for both riders. So the distance that Rachel travels is...

Gerry started two hours later, so her time must be represented as...

And knowing she traveled at 10 miles an hour, we can say that her distance is...

Now we find when they are equal...

Now distribute...

Subtract 8t from both sides, and add 20 to both sides...

And divide by 2...

Rachel traveled for t miles at 8 mph. If t=10, then Rachel traveled miles. 80 miles.
Gerry traveled 10t-20, or miles. Which is equal to 80 miles.
Pay attention to what the word problem is asking!
1. At what time did Gerry overtake Rachel?
She left at 10:00AM, and traveled for 10 hours, so she overtook her at 8:00PM
2.How far had they gone by then?
They had both traveled 80 miles.
Check your answer!
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