Question

A bicyclist heads east at 10km/h. After she has traveled 24.2 kilometers, another cyclist sets out in the same direction going 30km/h. About how long will it take the second cyclist to catch up to the first cyclist?

Answer 1

We know that the first cyclist has traveled 24.2 km at a speed of 10 km/h. Lets use the equation
`time= (distance)/(speed)` to find the time of the first cyclist:

`t= (24.2)/(10)`

`t=2.42`
So, we know that she has traveled for 2.42 hours.

We also know that after she has traveled for 2.42 hours another cyclist sets out in the same direction, so if
`t` represents the time of our first cyclist, the time of our second cyclist will be
`t-2.42`.

Now we are going to use the equation
`distance=(speed)(time)` to relate the speeds and times of the two cyclist:
For the first one:

`distance=10t` equation (1)
For the second one:

`distance=30(t-2.42)` equation (2)

Replace (1) in (2)

`10t=30(t-2.42)`
The only thing left now is solve for
`t`:

`10t=30t-72.6`

`-20t=-72.6`

`t= (-72.6)/(-20)`

`t=3.63`

We can conclude that the second cyclist will catch up the first cyclist after 3.63 hours.