a Can you write the time in terms of the distance and rate?
B
b Substitute the length of the loop into the expression that you found in Part A.
A
aExpression: 9+x/10+5+3x/10
l Simplified Expression: 7+2x/5
B
b 2.2 hours
Practice makes perfect
a We are told that Marina rides her bike at an average rate of 10 miles per hour. One day, she rides 9 miles and then rides around a large loop x miles long. On the second day she rides 5 miles and then rides around the loop three times. Let's write the total distances on these two days.
First Day:& 9+x miles
Second Day:& 5+ 3x miles
We want to write an expression to represent the total time that she spends those two days while she is riding. To do so, let's first remember the formula for time.
Time = Distance/Rate
Now we will identify the time in terms of the corresponding distances at the average rate of 10 miles per hour.
Distance
Rate
Time=Distance/Rate
9+x
10
9+x/10
5+3x
10
5+3x/10
Great! Let's finally add the corresponding time expressions up.
b We are asked to find the total time that she would ride on those two days if the loop is 2 miles long. To do so we will plug x= 2 into the expression that we found in Part A.
