Question

One cat went 10 miles further when traveling at 50 mph than a second car that traveled 2 hours longer at a speed of 40 mph. how long di the first cat travel?

Answer 1

So, the first car traveled for 9 hours.

I assume there might be a typo in your question, as you mentioned "cat" instead of "car." Assuming you meant "car," let's solve the problem:

Let
`\( D_1 \)` be the distance traveled by the first car (at 50 mph),
`\( D_2 \)` be the distance traveled by the second car (at 40 mph), and
`\( t_2 \)` be the time taken by the second car.

The first car went 10 miles further than the second car, so we can write an equation relating the distances:

`\[ D_1 = D_2 + 10 \]`

We also know that the second car traveled for 2 hours longer than the first car:

`\[ t_2 = t_1 + 2 \]`

Now, we can use the formula
`\( \text{distance} = \text{speed} * \text{time} \)` to express the distances in terms of speeds and times:

`\[ D_1 = 50t_1 \]`

`\[ D_2 = 40t_2 \]`

Substitute these expressions into the first equation:

`\[ 50t_1 = 40t_2 + 10 \]`

Now, use the relationship between
`\( t_1 \) and \( t_2 \)` from the second equation:

`\[ 50t_1 = 40(t_1 + 2) + 10 \]`

Solve for
`\( t_1 \)`:

`\[ 50t_1 = 40t_1 + 80 + 10 \]`

`\[ 10t_1 = 90 \]`

`\[ t_1 = 9 \]`