Answer:
Speed of Carol is 78 mph and that of Steve is 84 mph.
Step-by-step explanation:
Let the speed of Carol is x mph and that of Steve is (x + 6) mph.
If they move towards each other with that speed, then the resultant speed will be (x + x + 6) = (2x + 6) mph
With this resultant speed, they cover 405 miles in 2.5 hours.
So,
⇒ 2x = 156
⇒ x = 78 mph
So, speed of Carol is 78 mph and that of Steve is (78 + 6) = 84 mph. (Answer)
Using the concept of proportional, it is found that the value of x for the given similar triangles is 2.
<h3>What is a proportion?</h3>A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Since two triangles ΔACD and ΔABE are similar triangles, then their corresponding sides will be proportional.
Therefore, AC/ AB = AD / AE
By substituting the measures of the sides here;
AC/ AB = AD / AE
(x + 10) / 10 = (15 +3) / 15
15(x + 10) = 180
x + 10 = 12
x = 12 - 10
x = 2
Therefore, the value of x for the given similar triangles is 2.
More can be learned about proportions at;
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