Algebra word problem

Question

Two cars start driving in the same direction from the same place. If one travels 55 mph and the other 61 mph how long will it take them to be 24 miles apart?

Answer 1

At time: t

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Car 1 Distance: s₁ = v₁t ==> s₁ = 55t

Car 2 Distance: s₂ = v₂t ==> s₂ = 61t

Distance between Car 1 and Car 2: s = s₂ - s₁ ==> s = 61t - 55t ==> 24 = 61t - 55t ==> 24 = (61 - 55)t

==> 24 = (6)t ==> t = 24/6 ==> t = 4 hrs

Answer 2

Hi, Matthew!

Okay, so let's call the time it takes the cars, driving in the same direction, to be 24 miles apart.

So, one car is driving 61 mph and the other is driving 55 mph.

You want to know when the car going the fastest (61 mph) is 24 miles further than the car going 55 mph.

So, the equation would be:

61t = 55t +24

Next, solve for t by isolating the variable.

1st, subtract 55t from both sides of the equation:

61t -55t = 55t -55t + 24

6t = 24

Now, divide both sides by 6, to further isolate t:

6t/6 = 24/6

t=4

Therefore, it will take 4 hours for the first car to be 24 miles ahead of the 2nd car.

Now, let's check the answer:

61(4) =55(4) +24

244 = 220 +24

244 = 244

The answer is correct.