Andrea and Peter are riding their bicycles in the same direction on the same path. Andrea started 6 miles ahead of Peter and is traveling at a rate of 12 miles per hour. Peter is traveling at a rate of 14 miles per hour. After how many hours will Peter catch up to Andrea? Write and solve an equation to model the problem. Explain the meaning of the solution.

3 hours

Step-by-step explanation:

Step one:

given

Andrea started 6 miles ahead of Peter and is traveling at a rate of 12 miles per hour.

let the number of hours be x

and the total distance traveled be y

y=6+12x1

the initial distance is 6 miles

the distance traveled after x hours = 12x

Peter is traveling at a rate of 14 miles per hour.

y=14x2

the initial distance is 0 miles

the distance traveled after x hours = 14x

Step two:

let us equate the two expressions above

6+12x=14x

14x-12x=6

2x=6

divide both sides by 2

x=6/2

x= 3 hours

it will take 3 hours for both of them to cover the same distance

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9