Answer:
131.3 miles
Step-by-step explanation:
The two cars are moving from different directions. The total distance between the two cars = 118 miles + 256 miles = 374 miles.
Let us assume that the two cars meet at point O, let the distance between car c and O be d₁, the distance between car d and point O be d₂, hence:
d₁ + d₂ = 374 miles (1)
Let speed of car d be x mph, therefore speed of car c = 2x mph (twice of car d). If it take the cars t hours to meet at the same point, hence
For car c:
2x = d₁/t
t = d₁ / 2x
For car d;
x = d₂/t
t = d₂/ x
Since it takes both cars the same time to meet at the same point, therefore:
d₁/2x = d₂ / x
d₁ = 2d₂
d₁ - 2d₂ = 0 (2)
Solving equation 1 and 2 simultaneously gives d₁ = 249.3 miles, d₂ = 124.7 miles
Therefore the distance from point of meet to Boston = 249.3 - 118 = 131.3 miles
Both the cars will meet at 131.33 miles from Boston.
Given in the question,
Distance between two cars = 118 + 256 = 374 miles
Let these cars meet at a point P.
Let the distance between the car C and point P = 'x' miles
Therefore, distance between car D and point P = (374 - x) miles
Time taken 't' by car C to travel the distance 'x' miles,
[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]
[tex]t=\frac{x}{2v}[/tex] -------(1)
Time taken 't' by the car D to travel (374 - x) miles,
[tex]t=\frac{(374-x)}{v}[/tex] ---------(2)
Substitute the value of 't' from equation (2) to equation (1),
[tex]\frac{x}{2v}=\frac{374-x}{v}[/tex]
[tex]\frac{x}{2}=374-x[/tex]
[tex]\frac{3x}{2}=374[/tex]
[tex]x=249.33\text{ miles}[/tex]
From the picture attached,
Distance between Boston and the meeting point = (x - 118) miles
= 249.33 - 118
= 131.33 miles
Therefore, both the cars will meet at a point 131.33 miles distant from Boston.
Learn more about the system of equations here,
https://brainly.com/question/9942937?referrer=searchResults
