D=rt word problem

Question

There are 2 cars 550 miles apart and traveling towards eachother. They meet in 5 hours. If one cars speed is 5 mph faster than the other, find the speed of each car.

Answer 1

D = rt Let's say car #1 is faster than car #2, so r₁ = r₂ + 5.

They both travel for 5 hrs (t). D₁ is r₁ x t miles or 5r₁ miles, but r₁ = r₂ + 5, so substitute:

D₁ = 5(r₂ + 5) miles

D₂ is 5r₂ miles

D₁ + D₂ = 550, so 5(r₂ + 5) + 5r₂ = 550, then 5r₂ + 25 + 5r₂ = 550

10r₂ = 525, so r₂ = 52.5 mph and r₁ = r₂ + 5 = 52.5 + 5 = 57.5 mph

Check: Car #1 57.5 x 5 = 287.5 mi

Car #2 52.5 x 5 = 262.5 mi

Total is 550.0 mi

Answer 2

These used to really confuse me, too. Remember that both cars cover 550 miles total. One just goes a little farther than the other (the one travelling 5 mph faster).

d = rt

550 = 5(r + r + 5)

550 = 5(2r + 5)

550 = 10r + 25

10r = 525

r = 52.5 mph

r + 5 = 57.5 mph

Answer 3

F = S + 5

d=rt =5r = 550

r = 550/5 = 110 = F+S

F+S = 110

F-S = 5

add the two equations to get

2F = 115

divide both sides by 2

F = 57 1/2 mph for the Faster car

S = 52 1/2 mph for the Slower car

check the answers

in 5 hours the faster car goes 5x57.5 = 287.5

in 5 hours the slower car goes 5x52.5 = 262.5

5(57.5+52.5) = 5(110) = 550

287.5 + 262.5 = 550