MATHEMATICS HIGH SCHOOL

In one day, Annie traveled 5 times the sum of the number of hours brian traveled and 2. Together they traveled 20 hours. Find the number of hours each person traveled

Answers

Answer 1
Answer: Brian traveled 1 2/3 hours while Annie traveled 18 1/3 hours.

Explanation:
Let b be the number of hours Brian travels. Annie travles 5 times the sum of Brian's hours and 2, or 5(b+2). Together they travel 20 hours:
5(b+2)+b=20.

Use the distributive property:
5*b+5*2+b=20
5b+10+b=20.

Combine like terms:
6b+10=20.

Subtract 10 from both sides:
6b+10-10=20-10
6b=10.

Divide both sides by 6:
6b/6=10/6
b=5/3=1 2/3.

Brian travels 1 2/3 hours. This means Annie travels
5(1 2/3+2)=5(3 2/3)=5(11/3)=55/3=18 1/3 hours.
Answer 2
Answer:

Annie and Brian traveled 18.3 hours and 1.7 hours respectively

Further explanation

Simultaneous Linear Equations can be solved using one of the following methods :

  • Elimination Method
  • Substitution Method
  • Graph Method

Let's try to solve the problem now.

Let :

Annie's number of hours = A

Brian's number of hours = B

If Annie traveled 5 times the sum of the number of hours brian traveled and 2 , then it could be written as :

\boxed {A = 5 * ( B + 2 )} → Equation 1

If together they traveled 20 hours , then it could also be written as :

\boxed {A + B = 20}

5 * ( B + 2 ) + B = 20  ← Equation 1

5B + 10 + B = 20

6B = 20 - 10

6B = 10

B = 10 / 6

B = (5)/(3) ~ hours

\boxed {\boxed {B \approx 1.7 ~ hours} }

A = 5 * ( (5)/(3) + 2 )

A = 5 * ( (5)/(3) + (6)/(3) )

A = 5 * ( (11)/(3) )

A = (55)/(3)

\boxed {\boxed {A \approx 18.3 ~ hours} }

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Elimination , Substitution , Graph , Method , Linear , Equation , Simultaneous

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