Question

TWO HOURS AFTER HARLAN HAD LEFT HIS HOUSE FOR HIS OUT OF STATE BUSINESS TRIP, HIS WIFE MAGGIE NOTICED HE HAD FORGOTTEN HIS BRIEFCASE. KNOWING THAT THE BRIEFCASE CONTAINED ALL OF HIS IMPORTANT PAPERS, SHE IMMEDIATELY HOPPING INTO HER CAR AND BEGAN TO CHASE AFTER HIM AT A SPEED OF 65 MPH. IF HARLAND DROVE 55 MPH THE ENTIRE TIME, HOW MANY HOURS DID IT TAKE MAGGIE TO CATCH HIM??

Answer 1

Let’s denote the time it took Maggie to catch Harlan as \( t \) in hours. Since Harlan left two hours before Maggie, the total time that Harlan has been driving by the time Maggie catches up is \( t + 2 \) hours.

During the time Harlan is driving, the distance he covers can be expressed as: \[ \text{Distance}_H = \text{Speed}_H \times \text{Time}_H = 55(t + 2) \]

The distance Maggie covers while chasing him is: \[ \text{Distance}_M = \text{Speed}_M \times \text{Time}_M = 65t \]

Since Maggie catches up with Harlan, the distances they covered are equal: \[ 55(t + 2) = 65t \]

Now, we can expand and simplify the equation: \[ 55t + 110 = 65t \]

Then, we rearrange it to solve for \( t \): \[ 110 = 65t - 55t \ 110 = 10t \ t = 11 \]

Therefore, it took Maggie 11 hours to catch Harlan.