To determine how many hours it took for Penny to be 5 miles ahead of Darla, we start by defining their rates of travel and the relationship between the distances they cover over time.
1. Darla's speed \( v_D \) = 65 mph
2. Penny's speed \( v_P \) = 70 mph
3. The time it takes for Penny to be 5 miles ahead of Darla is \( t \) hours.
Since both leave the office at the same time and travel in the same direction, the distance each travels after \( t \) hours can be expressed as:
- Distance traveled by Darla: \( D_D = 65t \)
- Distance traveled by Penny: \( D_P = 70t \)
We need to find the time \( t \) when Penny is 5 miles ahead of Darla, which means \( D_P = D_D + 5 \):
\[ 70t = 65t + 5 \]
To isolate \( t \), we subtract \( 65t \) from both sides:
\[ 70t - 65t = 5 \]
\[ 5t = 5 \]
Now, divide both sides by 5:
\[ t = 1 \]
Therefore, it takes **1 hour** for Penny to be 5 miles ahead of Darla.
darla and her friend penny left their office at the same time and began traveling down the same road in the same direction. Darla traveled at a speed of 65 mph while penny drove at 70 mph. How many hours was it before penny was 5 miles ahead of darla?
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