One more "easy" AP Physics question....?

Question

The question:A car moving at 65 mi/h passes a pickup truck moving at 50 mi/h. The car goes on for 30 mi, then stops at a rest stop for 20 min. The car resumes its journey, again at 65 mi/h. Assuming the truck did not stop and maintained its speed, did it pass the car while it was stopped? (You may solve this problem by graphical means.)

The answer to this is yes. It's the follow up question I'm having trouble with:

If so, how long after the initial passing does it take for the car to catch the truck again?

Here is where I've gotten:

1. Calculated that the truck reaches the car .6h (36 minutes) after the car passes the truck.

2. Found that the car resumes travel .793h (47.6 minutes) after it passed the truck.

3. At the time at which the car resumes travel, it is 9.66665 miles behind the truck.

4. To solve for the time needed to catch up with the truck, I calculated .64444h (38.65 minutes). I found this by: 9.6665/15m (the distance between car and truck divided by the difference in speed in mph).

However, the homework is done online and I that particular question was marked wrong when I submitted my answer. Where did I go wrong? Thanks for the help!

Answer 1

find out how far truck has travelled when car gets to rest stop

car takes 30/65 of a hour to travel 30 mi (use d/v = t)

now the truck will have travelled 30/65 * 50 = 23/1/13 miles

now for the next 20 minutes (1/3 hour) the car goes nowhere but truck moves

(1/3) * 50 = 16/2/3 miles

so it has travelled 23/ 1/ 13 + 16/ 2/ 3 = 39/29/39 miles or is 9/29/39 miles ahead of car

now find out when car reaches truck again (they will have travelled the same distance for car to catch up so)

9/29/39 + 50 t = 65 t (t is time to catch up)

9/29 /39 = 15 t

t = 76/117 hours

so total time = 30/65 + 1/3 + 76 / 117 = 1/4/9  hour

so it takes 1 hour and 26 minutes 40 seconds to catch up to truck again

your calculations seem correct but your use of decimals probably caused inaccuracy in your final answer, also i don't think it is neccessary for step 1 of your calculations where you find out when car reaches truck because this information does not help you in reaching the final answer , in fact this info along with so much of the other info could confuse you so don't calculate things that are not neccessary!

hope this helps