In one day ,anne traveled 5 times the sum of the number of hours Brian traveled and 2 .together they traveled 20hours find the number of hours each person traveled

Answer 1

b represents the hours Brian traveled

5(b + 2) represents the hours Anne traveled

b + 5(b + 2) = 20

b + 5b + 10 = 20

6b = 10

b = 1 2/3

Brian traveled 1 hour 40 minutes

Anne traveled 18 hours 20 minutes

Answer 2

The first step is translate what information is given into an equation.

For variables, we will use "A" for the number of hours Anne traveled and "B" for Brian's.

"Anne traveled 5 times the sum of the number of hours Brian traveled and 2." This expression would look like:

A = 5B + 2

"Together they traveled 20 hours." This means we need to write an equation so that A + B = 20. In the previous step, I wrote an equation that showed how many hours Anne traveled based on how many hours Brian traveled.

A = 5B + 2

A + B = 20

Substitute A = 5B + 2 into the second equation

5B + 2 + B = 20

Add like terms on both sides.

6B + 2 = 20

6B = 18

B = 3

So now we know that Brian traveled for 3 hours. Since we have this information, we can now find out how many hours Anne traveled with the equation from the first step.

B = 3

A = 5B + 2

Substitute B into the second equation.

A = 5(3) + 2

A = 15 + 2

A = 17

So the answers are: Brian traveled 3 hours and Anne traveled 17 hours.