Question

Question #6c6cc

Answer 1

1.5 Hours

Explanation:

The best way to tackle this problem is to create a system of equations to model the scenario. Let's start by creating Bob's equation. We want an equation for his distance in terms of time spent (hours), so:

`d=30t` where `t` is time in hours once Bob starts

But, since Sharon is letting him have a lead of half an hour, we need to know how far ahead Bob is before Sharon starts. Using the equation above and plugging in 0.5 for `t`, we get that Bob traveled 15 miles before Sharon started. So we can modify our equation to be the following:

`d=30t+15` where `t` is time in hours once Sharon starts (so when Sharon begins, `t=0`).

Now, let's create an equation for Sharon's distance in terms of time spent (hours):

`d=40t` where `t` is time in hours once Sharon starts

Now we set these two equations equal to each other, since we know when they catch up with each other their distances traveled (from when Sharon starts) will be equal, so:

`d=30t+15` and `d=40t` where `d` is equal,
`30t+15=40t`
`30tcolor(red)(-30t)+15=40tcolor(red)(-30t)` Subtract `30t` from both sides
`15=10t`
`15/color(red)(10)=(10t)/color(red)(10)` Divide 10 from both sides
`1.5=t`

Hope this helped!