Answer:
The correct statements are:
- Armand and Jill will travel the same amount of time to meet.
- The equation used to find the time, t, it will take for them to meet is 50t + 60t = 247.5.
- Jill will travel 135 miles to meet Armand.
Step-by-step explanation:
It is given that:
Armand and Jill are 247.5 miles apart, and driving toward each other.
Armand is driving at a rate of 50 miles per hour.
and Jill is driving at a rate of 60 miles per hour.
Let they meet after t hours.
We know that Distance= Speed×Time
so distance covered by Armand=50t
and Distance covered by Jill=60t.
Now as they are travelling towards each other so:
50t+60t=247.5--------------(a)
1)
Armand and Jill will each travel the same distance to meet.
This statement is wrong as the value of 50t and 60t will be different for the same t.
2)
Armand and Jill will travel the same amount of time to meet.
This statement is true as they will meet at the same time.
3)
The equation used to find the time, t, it will take for them to meet is 50t + 60t = 247.5
This statement is correct.
4)
It will take 4.5 hours for them to meet.
We will find the value of t from equation (a) and check whether the value of t=4.5 or not.
As 50t+60t=247.5
⇒ 110t=247.5
⇒ t=247.5/110=2.25
Hence it will take 2.25 hours for both of them to meet.
Hence, option 4 is incorrect.
5)
Jill will travel 135 miles to meet Armand.
The distance travel by Jill to meet Armand=60t
As t=2.25
⇒ 60t=60×2.25=135 miles.
Hence, option 5 is true.
