Question

Joan left Durham traveling 85 mph. Mike,to catch up,left some time later driving at 94 mph. Mike caught up after 7 hours. How long was Joan driving before Mike caught up?

Answer 1

Joan had been driving for `7`hours `44`mins

Explanation:

*Before we start we should immediately note that `"speed, distance and time"` are all present in the question. Therefore we know we will most likely need to use the equation: `"Speed"="Distance"/"Time"`

Firstly let's call the place where the two people meet `x`.

To get to point `x` Joan travelled at `85mph` for `y` amount of time.

To get to point `x` Mike travelled at `94mph` for `7` hours.

Mike has given us both `"speed and time"` We can, therefore, now work out the distance Mike meets Joan.
-Rearrange the formula :`"Distance"="Speed" times "Time"`

`"Distance"=94 times 7`

`"Distance"=658"miles"`

We now know that the point they both meet at (which we called `x` to start with is: `658`

We now know the `"Distance and Speed"` of Joan. We can, therefore, work out the length of time Joan has been travelling.
-Rearrange the formula: `"Time"="Distance"/"Speed"`
`"Time"=658/85`

`"Time"=7.74"hours"(2.D.P.)`

Now all that remains for us to do is work out how many minutes Joan has been travelling for.

`"mins"/60 times 100=74`

`"mins"/60=74/100`

`"mins"=74/100 times 60`

`"mins"=44`

Joan has therefore been travelling for `7`hours `44`mins