Solution-
Two cars leave the same location traveling in opposite directions.
The first car leaves at 3 p.m and has a speed of 55 mph
The second car leaves at 4 p.m and has a speed of 75 mph
Let x hours after the first car leaves, the two cars are 380 miles apart from each other.
[tex]Speed =\frac{Distance}{Time}[/tex]
[tex]\Rightarrow Distance=Speed\times Time[/tex]
In this x hours, distance covered by the first car,
[tex]\Rightarrow Distance_1=Speed_1\times Time_1[/tex]
[tex]\Rightarrow Distance_1=55\times x[/tex]
As the second car leaves at 4 p.m i.e 1 hour late as compared to the first car, so distance covered by the second car in (x-1) hours,
[tex]\Rightarrow Distance_2=Speed_2\times Time_2[/tex]
[tex]\Rightarrow Distance_2=75\times (x-1)[/tex]
According to the question,
[tex]Distance_1+Distance_2=380[/tex]
[tex]\Rightarrow 55\times x+75\times (x-1)=380[/tex]
[tex]\Rightarrow 55x+75x-75=380[/tex]
[tex]\Rightarrow 130x=455[/tex]
[tex]\Rightarrow x=3.5[/tex]
∴ After 3.5 hours from 3 p.m i.e at 6.5 p.m the cars will have a distance of 380 miles.
