Bill starts riding his bike towards town at a constant rate of 8 mph. Then, 30 minutes later, his wife starts driving on the same path at a constant average of 30 mph. How long will it take her to catch up to Bill?
This question is from a study packet, that also has the answer shown as
8(.5)/30-8 = approx. 18 hours = approx. 10.8 mins = approx 10 minutes 48 seconds.
When I solve the problem that way, I understand the answer. However, based on my understanding of DRT problems, that doesn't seem correct. The way I solve this is using a table
Persons R T D
Bill 8mph t 8(t)
Wife 30mph t-.5 30(t-.5)
8t=30(t-.5)
=8t=30t-15
=-22t=-15
=-15/-22
=.68
You can solve it that way with the table. However, you should understand that you named "t" as the time Bill takes to get to the "meeting point."
This is correct, but the question asks for the time his WIFE took to catch up to Bill. Therefore, you now need to calculate t - .5, which is the
time you have for the wife. When you do that, you get: .68 - .5 = .18 of an hour, which when multiplied by 60, gives you about 10.8 minutes,
which is the correct answer.
To make it less confusing and get straight to the answer, I would suggest that you let the wife's time be "t." That way, when you get "t,"
you will have your answer. The table would then look like this:
Persons R T D
Bill 8mph t+.5 8(t + .5)
Wife 30mph t 30(t)