A family drove 1080 miles to their vacation lodge. Because of increased traffic density, their average speed on the return trip was decreased by 6 miles per hour and the trip took 2.5 hours longer. Determine their average speed on the way to the lodge.
Can someone help define a variable and write an equation?
Sure, we can help with that.
Let V be the average speed GOING to the ladge, a distnce d = 1080 miles away.
V * T = 1080
(V-6)*(T+2.5) = 1080
Substitute 1080/V for T in the second equation and solve for V.
To solve this problem, we can define a variable and write an equation to represent the given information.
Let's assume the average speed on the way to the lodge is "x" miles per hour.
Now, let's consider the facts stated in the problem:
1. The family drove a total of 1080 miles to their vacation lodge.
2. On the return trip, their average speed decreased by 6 miles per hour.
3. The return trip took 2.5 hours longer than the trip to the lodge.
Based on this information, we can write an equation to represent the situation.
Distance = Speed × Time
For the trip to the lodge:
Distance = 1080 miles
Speed = x miles per hour
Time = Distance / Speed = 1080 / x hours
For the return trip:
Distance = 1080 miles
Speed = (x - 6) miles per hour
Time = Distance / Speed = 1080 / (x - 6) hours
Since the return trip took 2.5 hours longer than the trip to the lodge, we can set up the following equation:
1080 / x = 1080 / (x - 6) + 2.5
Now, you can solve this equation to find the value of "x," which represents the average speed on the way to the lodge.