Two trucks are driving to the same place. The first truck starts 50 miles ahead of the second truck and travels at an average speed of 60 miles per hour. The second truck travels at an average speed of 70 miles per hour. Which graph represents this situation and shows the number of hours it will take for the second truck to pass the first truck?
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To find out when the second truck passes the first truck, we need to set up an equation based on their speeds and distances.
1. Distance formula: Distance = Speed × Time.
2. Truck 1: Starts 50 miles ahead and travels at 60 mph. Distance after t hours = 50 + 60t.
3. Truck 2: Starts behind and travels at 70 mph. Distance after t hours = 70t.
To find when Truck 2 catches up to Truck 1, set the distances equal:
[ 50 + 60t = 70t ]
Now, simplify and solve for t:
1. Subtract 60t from both sides:
[ 50 = 70t – 60t ]
[ 50 = 10t ]
2. Divide by 10:
[ t = 5 ]
So, the second truck will pass the first truck after 5 hours.
For the graph, look for the one that shows Truck 2’s line intersecting Truck 1’s line at the 5-hour mark, along with the corresponding distances.
Check your answer choices to find the graph that represents this scenario accurately.
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