in one day Annie travels 5 times the sum of the number of hours brian traveled and 2. together they traveled 20hrs. find the numbers hours they each traveled

Answer 1

A = hours Annie travels

B = hours Brian travels

From the problem we know that Annie travels 5 times the sum of Brian's hours plus 2

A = 5(B+2)

We know that together they traveled 20 hours

A + B = 20

If we substitute the first equation into the second we get

5(B+2) + B = 20

5B + 10 + B = 20

6B = 10

B = 5/3 hours

If we put that back into the first equation

A = 5(B+2)

A = 5(5/3 + 2)

A = 5 (11/3)

A = 55/3

Answer 2

Let's assign these people variables.

Let's say Annie Travels A hours and Brian Travels B hours.

We know from the second sentence that A + B = 20

Next, Let's parse our the first sentence, I always find it easiest to start at the end of these sentences and build an equation that way.

"the sum of the number of hours Brian traveled and 2" → B +2

"Five times the sum... " 5 * (B+2)

Annie Travels → A = 5 * (B+2)

Now we need to substitute one equation into the other.

It's true that A = A right? Then set the A in A + B to the A from our second equation.

A + B → 5*(B+2) + B = 5 & then rearrange to solve for B!