Question

A spy realizes his cover is blown and flees toward his secret evacuation spot at a speed of 60 mph. Two hours later, a special agent in a helicopter starts chasing the spy. the secial agent travels the same route at a speed of 90 mph.
what distance does the spy cover in t hours?

Answer 1

To find the distance the spy covers in \( t \) hours, we can use the formula for distance:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

The spy travels at a speed of 60 mph. Since he has a 2-hour head start before the special agent starts chasing him, we need to account for that in the total time he has traveled when the agent starts chasing.

If we denote the time the special agent has been chasing the spy as \( t \) hours, then the total time the spy has been traveling by that time is \( t + 2 \) hours (because he started 2 hours earlier).

Now, the distance covered by the spy can be calculated as follows:

\[
\text{Distance covered by the spy} = \text{Speed of spy} \times \text{Total time traveling}
\]
\[
\text{Distance covered by the spy} = 60 \text{ mph} \times (t + 2) \text{ hours}
\]

Therefore, the distance \( d \) the spy covers in \( t \) hours is given by:

\[
d = 60(t + 2)
\]

If you want to simplify it further, it can be expressed as:

\[
d = 60t + 120
\]

So, the distance the spy covers in \( t \) hours is \( 60t + 120 \) miles.