To solve this problem, we need to set up an equation based on the total distance Terry traveled and the fact that he drove at two different speeds for different portions of the trip. Here's how to approach it:

Variables

Let:

• $t_1$ be the time (in hours) Terry spent driving at 60 km/h.
• $t_2$ be the time (in hours) Terry spent driving at 50 km/h.

We are given the following information:

• The total distance is 390 km.
• The total time is 7 hours.
• The first part of the trip was at 60 km/h, and the second part was at 50 km/h.

Equations

1. The total time spent driving: $t_1 + t_2 = 7 \text{ hours}$

2. The total distance covered: $60t_1 + 50t_2 = 390 \text{ km}$

Solve the system of equations

From the first equation: $t_1 = 7 - t_2$

Substitute this into the second equation: $60(7 - t_2) + 50t_2 = 390$

Simplify and solve for $t_2$: $420 - 60t_2 + 50t_2 = 390$ $420 - 10t_2 = 390$ $-10t_2 = 390 - 420$ $-10t_2 = -30$ $t_2 = 3$

So, Terry spent 3 hours driving at 50 km/h.

Why the answer is 3 hours

This result comes from solving the system of equations that accounts for both the total time spent and the total distance traveled, considering the two different speeds.

Would you like a breakdown of how the speed-distance relationship worked here, or any clarification?

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Here are 5 related questions to further explore this concept:

1. How much distance did Terry cover while driving at 60 km/h?
2. If Terry had driven at a constant speed of 55 km/h, how long would the trip have taken?
3. How would the total time change if Terry had driven the entire trip at 50 km/h?
4. What would have happened if the speed during the thunderstorm dropped to 40 km/h?
5. If Terry had taken a break for 1 hour, how would that affect the total time?

Tip: When dealing with different speeds over portions of a trip, always break down the problem into time and distance for each part to set up your equations effectively.