Question

Car A travels 20 mph faster than Car B. In the same time that Car A travels 208 mi, Car B travels 156 mi. Find their speeds. The speed of Car A is and the speed of Car B ​

Answer 1

`\huge\colorbox{red}{Car\: A=80}\colorbox{blue}{Car B=60}`

Explanation:

to understand this

you need to know about:

• equation
• PEMDAS

let's solve:

let the speed of car A be A

let the speed of car B be B

according to the first condition:

`\quad A=B+20`

according to the second condition:

`\quad 156(A)=208B`

1. 
   `\text{substitute the value of A into the equation:}\\ \sf \implies 156(B+20)=208(B)`
2. 
   `\sf distribute:\\ \implies 156B+3120=208B`
3. 
   `\sf \: substract\: 156B \: from \: both \: sides : \\ \implies \: 156 B -156 B + 3120 = 208 B - 156 B \\ \implies \: 3120 = 52 B`
4. 
   `\sf divide \: both \: sides \: by \: 52 : \\ \implies (52B)/(52) = (3210)/(52) \\ \therefore \: B = 60`

therefore

`\text{the speed of car A is 60+20=80}`

Answer 2

Explanation:

Assuming the speed of car B to be x and the speed of car A to be x+20

156 = 208

x. x+20

156(x+20)= 208x

156x+3120=208x

3120=208x-156x

3120=52x

x=60

The speed of car A is (x)= 60

The speed of car B is(x+20)= 80