Question 1006347
rate * time = distance.


when david catches up with carlton, they both will have jogged the same amount of time.


the distance that carlton jogs will be 2 less than the distance that david jogs because carlton has already jogged 2 miles and david needs to run that same 2 miles plus whatever carlton continues to jog in order to catch up.


let R1 * T1 = D1 be the rate * time = distance formula for carlton.
let R2 * T2 = D2 be the rate * time = distance formula for david.


since the time each will jog once david starts jogging is the same, then let T = T1 = T2 and the formulas become:


R1 * T = D1
R2 * T = D2


since carlton needs to jog 2 miles less than david needs to jog after david starts jogging, then D1 = D2 - 2


the formulas become:


R1 * T = D2 - 2
R2 * T = D2


you are told that carlton's rate is .1 miles per minute and that david's rate is .2 miles per minute.


the formulas become:


.1 * T = D2 - 2
.2 * T = D2


solve each of these formulas for T and you get:


T = (D2 - 2) / .1
T = D2 / .2


replace T in the first equation with the equivalent value of D2 / .2 from the second equation to get:


D2 / .2 = (D2 - 2) / .1


cross multiply to get:


.1 * D2 = .2 * (D2 - 2)


divide both sides of this equation by .1 to get:


D2 = 2 * (D2 - 2)


simplify to get:


D2 = 2 * D2 - 4


subtract D2 from both sides of this equation and add 4 to both sides of this equation to get:


4 = 2 * D2 - D2


simplify to get:


4 = D2


this can also be shown as:


D2 = 4


D2 is how far david needs to run.


D1 = how far carlton has run after david has run 4 miles.


D1 = D2 - 2 = 4 - 2 = 2


this means that carlton will have run 2 miles when david catches up to him.


carlton will have jogged 2 more miles after david starts.
david will have jogged 4 miles when he catches up with carlton.


you can solve the the time as well.


you get for carlton, rate * time = distance becomes .1 * T = 2.
this gets you T = 2/.1 = 20 minutes.


you get for david, rate * time = distance becomes .2 * T = 4.
this gets you T = 4/.2 = 20 minutes.


they both run for 20 minutes when david catches up to carlton.


carlton has run .1 * 20 = 2 miles.
david has run .2 * 20 = 4 miles.