Deb is biking to school, but she forgot her lunch. When her dad leaves the house to bring her lunch, Deb is already 1.2 miles from home and is biking at a speed of 13 miles per hour. Her dad drives at a speed of 25 miles per hour.

Question

If they each keep a constant speed, how many hours will it take for Deb's dad to catch up to her?
Simplify any fractions.

Answer 1

Let's denote the time it takes for Deb's dad to catch up to her as \( t \) hours.

Step 1: Set up the equations for the distances.

• The distance Deb travels in \( t \) hours is given by her speed multiplied by time: \[ \text{Distance Deb} = 1.2 + 13t \] (She starts 1.2 miles from home and bikes at 13 mph.)

• The distance her dad travels in the same time \( t \) is: \[ \text{Distance Dad} = 25t \] (He starts from home and drives at 25 mph.)

Step 2: Set up the equation where their distances are equal.
To find out when Deb's dad catches up to her, we set the distances equal to each other: \[ 1.2 + 13t = 25t \]

Step 3: Solve for \( t \).
Rearranging the equation gives: \[ 1.2 = 25t - 13t \] \[ 1.2 = 12t \]

Now, divide both sides by 12: \[ t = \frac{1.2}{12} \] \[ t = 0.1 \]

Step 4: Simplify \( t \).
Converting 0.1 hours to minutes: \[ 0.1 \times 60 = 6 \text{ minutes} \]

Thus, it will take Deb's dad 0.1 hours or 6 minutes to catch up to Deb.