Question

Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD’s vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system? [Official GMAT-2018]

Hint:

When working with problems involving distance, rate, and time, use the formula \( \text{Distance} = \text{Rate} \times \text{Time} \).

Answer 1

Step 1: Define the variables.
Let \( t \) represent the time in hours after 8:00 a.m. that the dispatcher retrieved the data.
Step 2: Calculate the distances driven by Al and Ben.
- Al left SD at 11:00 a.m., so the time he has been driving is \( t - 3 \) hours.
- Al’s distance = 40 miles per hour \(\times (t - 3)\) hours.
- Ben has been driving for \( t \) hours.
- Ben’s distance = 20 miles per hour \(\times t\) hours.
Step 3: Set up the equation.
The total distance driven by both Al and Ben is 240 miles, so we have: \[ 40(t - 3) + 20t = 240 \] Simplifying this equation: \[ 40t - 120 + 20t = 240 \quad \Rightarrow \quad 60t = 360 \quad \Rightarrow \quad t = 6 \] Step 4: Conclusion.
The dispatcher retrieved the data 6 hours after 8:00 a.m., which is at 2:00 p.m.