Question 1038326
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 {{{D=RT}}}. And we know that the distance is the same for both riders. So the distance that Rachel travels is...
{{{D=8t}}}
Gerry started two hours later, so her time must be represented as...
{{{t-2}}}
And knowing she traveled at 10 miles an hour, we can say that her distance is...
{{{D=10(t-2)}}}
Now we find when they are equal...
{{{8t=10(t-2)}}}
Now distribute...
{{{8t=10t-20}}}
Subtract 8t from both sides, and add 20 to both sides...
{{{20=2t}}}
And divide by 2...
{{{10=t}}}
Rachel traveled for t miles at 8 mph. If t=10, then Rachel traveled {{{8*10}}}miles. 80 miles.
Gerry traveled 10t-20, or {{{(10*10)-20}}}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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