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?
1.
2.
3.
4.
To determine which graph represents the situation, let’s analyze the scenario:
1. The first truck starts 50 miles ahead and travels at 60 mph.
2. The second truck starts from a point 50 miles behind and travels at 70 mph.
To find out when the second truck will catch up with the first truck, we can set up an equation. Let ( t ) be the time in hours:
– Distance traveled by the first truck: ( 60t + 50 ) (starts 50 miles ahead)
– Distance traveled by the second truck: ( 70t )
We want to find ( t ) when both have traveled the same distance:
[ 70t = 60t + 50 ]
Now, subtract ( 60t ) from both sides:
[ 10t = 50 ]
Now, divide both sides by 10:
[ t = 5 ]
So, it will take the second truck 5 hours to catch up with the first truck.
In terms of a graph, you would want to look for a graph where the line representing the distance of the second truck crosses the line representing the distance of the first truck at the 5-hour mark.
If you have options for graphs, the correct graph would show the point of intersection at ( t = 5 ) hours.
If you need more assistance analyzing specific graphs, please refer to the extended services page.