Question

Tony and Bill are 1,725 miles apart and headed straight toward each other. If Tony is traveling at 55mph and Bill is traveling at 60mph, how many hours will it be before the two cars are side-by-side?

Answer 1

To find how many hours it will be before Tony and Bill’s cars are side-by-side, we can use the following formula:

Time = distance / relative speed

Because Tony and Bill are traveling toward each other, the relative speed is the sum of their speeds:

55mph + 60mph = 115mph

We now can plug our given values into the equation:

1,725 / 115 = 15

which represents our time in intervals of hours. Therefore, it will take 15 hours before the two cars are side-by-side.

Answer 2

To solve this problem, we will use the formula:

`\qquad\quad\boxed{\text{Time} = \frac{\text{Distance}}{\text{Rate}}}`

In this case, we want to find the time it will take for Tony and Bill to meet, so we need to find the distance they will travel before they meet.

Since they are headed straight toward each other, the combined distance they will travel is equal to the total distance between them: 1,725 miles.

Let's call the time it takes for them to meet "t". Then we can write two equations:

`\qquad\begin{gathered}\text{Distance}_\text{Tony} = \text{Rate}_\text{Tony} \cdot t\\\text{Distance}_\text{Bill} = \text{rate}_\text{Bill} \cdot t\end{gathered}`

We know that the sum of their distances is 1,725 miles, so we can write the equation:

`\text{Distance}_\text{Tony} + \text{Distance}_\text{Bill} = 1,725`

Substituting the first two equations into the third equation, we get:

`(\text{Rate}_\text{Tony} \cdot t) + (\text{Rate}_\text{Bill} \cdot t) = 1,725`

Simplifying, we get:

`\qquad\quad\begin{gathered}(55 + 60) \cdot t = 1,725\\115 \cdot t = 1,725\\t = (1,725)/(115)\\\boxed{t = 15\: \text{hours}}\end{gathered}`

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