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?

*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