Answer:
x=4
Step-by-step explanation:
We are given that the triangles are congruent.
Specifically, the order of the letters gives that the angles ∠DAB and ∠CBA are corresponding parts of the two congruent triangles. Since corresponding parts of congruent triangles are themselves congruent, ∠DAB ≅ ∠CBA. Thus, m∠DAB = m∠CBA.
Given the expressions for the two angles, we can substitute into the equation, and solve for the requested variable.
Average speed of slower car = 60 mph
Average speed of faster car = 70 mph
<em><u>Solution:</u></em>
Given that Two cars enter the Delaware turnpike at shoreline drive at 8 am, each heading for ocean city
Given that One cars average speed is 10 mph faster than the other
Let "x" be the average speed of slower car
Then x + 10 is the average speed of faster car
The faster car arrives at ocean city at 11 am, a half hour before the slower car
<em><u>Time taken by faster car:</u></em>
The faster car arrives at ocean city at 11 am but given that they start at 8 a.m
So time taken by faster car = 11 am - 8am = 3 hours
<em><u>Time taken by slower car:</u></em>
The faster car arrives at ocean city at 11 am, a half hour before the slower car
So slower car takes half an hour more than faster car
Time taken by slower car = 3 hour + half an hour =
Now the distance between Delaware turnpike at shoreline drive and ocean city will be same for both cars
Let us equate the distance and find value of "x"
<em><u>The distance is given by formula:</u></em>
<em><u>Distance covered by faster car:</u></em>
<em><u>Distance covered by slower car:</u></em>
Equating both the distance,
3x + 30 = 3.5x
3x - 3.5x = -30
-0.5x = -30
x = 60
Thus average speed of slower car = 60 mph
Average speed of faster car = x + 10 = 60 + 10 = 70 mph