Respuesta :
Answer:
speed of car A =Speed of car B=0.8 miles/minutes.
Step-by-step explanation:
We are given that speed of car A is equal to speed of car B.
Also let car A travels x miles.
and car B travels y miles.
Car A reaches its destination in 17 minutes.
this means that speed of car A is given by: [tex]\dfrac{x}{17}[/tex] miles/minutes ( since speed is defined as the ratio of distance and time).
Car B reaches its destination in 32 minutes.
This means that the speed of car B is given by: [tex]\dfrac{y}{32}[/tex] miles/minutes
as speed of both cars are equal this means:
[tex]\dfrac{x}{17}=\dfrac{y}{32}[/tex]------(1)
Also we are given Car B travels 12 miles farther than Car A.
this means [tex]y-x=12[/tex]
[tex]y=12+x[/tex]------(2)
on using equation (1) and (2) we have:
[tex]\dfrac{x}{17}=\dfrac{12+x}{32}\\ \\32x=17(12+x)\\\\32x=17\times12+17x\\\\32x-17x=17\times12\\\\15x=122\times17\\\\x=13.6[/tex]
Hence the speed of car A is 0.8 miles/minutes ( since x/17 is the speed of car A)
Speed of car B=0.8 miles/minutes.
You can use the fact that both the cars were travelling at the same speed so we can take them equal to some variable.
The speed of the cars was 0.8 miles per hour
How to form mathematical expression from the given description?
You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
How to find the speed of the cars?
Supposing that both the cars were travelling with the speed [tex]x \: \rm \text{miles/hour}[/tex]
Let the first car travels [tex]d_1[/tex] miles
then as second car travels 12 miles extra, thus, distance traveled by second car is [tex]d_2 = d_1 + 12[/tex] miles.
Using the formula for speed, we have:
[tex]Speed = \dfrac{\text{Distance traveled}}{\text{Time taken}}[/tex]
- For first car:
Distance traveled = [tex]d_1[/tex] miles
Speed = [tex]x \: \rm miles[/tex]
Time taken = [tex]17 \: \rm minutes[/tex]
Thus,
[tex]x = \dfrac{d_1}{17} \: \rm miles/hour[/tex]
- For second car:
Distance traveled = [tex]d_2 = d_1 + 12[/tex] miles
Speed = [tex]x \: \rm miles[/tex]
Time taken = [tex]32 \: \rm minutes[/tex]
Thus,
[tex]x = \dfrac{d_1 + 12}{32} \: \rm miles/hour[/tex]
So, we got system of 2 linear equations in two variables.
Using the expression for x from first equation and substituting it in second equation, we get
[tex]x = \dfrac{d_1 + 12}{32}\\\\\dfrac{d_1}{17} = \dfrac{d_1 + 12}{32}\\\\\dfrac{32}{17}d_1 - d_1 = 12\\\\d_1 = \dfrac{12 \times 17}{15} = \dfrac{68}{5} = 13.6 \: \rm miles[/tex]
Substituting this value in first equation to get the value of x
[tex]x = \dfrac{d_1}{17}\\\\x = \dfrac{13.6}{17} = 0.8 \: \rm miles/hour[/tex]
Thus,
The speed of the cars was 0.8 miles per hour
Learn more about system of linear equations here:
https://brainly.com/question/13722693
