Jen and karen are travelling for the weekend. they both leave from jen's house and meet at their destination. jen drives 45mph the whole way. karen drives 60mph but leaves a half hour after jen. how long after jen leaves does karen catch up with her?

For this case what we should do is write the equation of movement for each one.
 We have then:
 For Jen:
 r = 45 * t
 For Karen:
 r = 60 * (t-0.5)
 Equating equations we have:
 45 * t = 60 * (t-0.5)
 Clearing time:
 60t - 45t = 30
 15t = 30
 t = 30/15
 t = 2 hours
 
 karen catches up with her after 2 hours.

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