Car A and B travel a distance, who gets there first?

Question

If two cars leave the same house at the same time, they will be traveling along on two roads to get to their destination, the first road, has a speed limit of 15mph, and it is 1/4 of the overall distance to their destination, the second road has a speed limit of 45mph, and it covers the remaining 3/4 of the distance.

now, Car A stops for gas halfway during the 1st leg of the trip (during the 15mph zone), while Car B continues on. after a Time Gap A, Car A continues on its path. Currently trailing Car B

Car B then stops for gas halfway through the 2nd leg (the 45mph zone) and stops for the same amount of time (Time Gap A), after continuing on its journey, both Car A and Car B arrive at their destination.

The question is, do they arrive at the same time? and if not, who wins? and if you can, why exactly?

think about this, Car B gets to the 45mph zone first, and thus, spends time in this zone while Car A is still going slower, this way, Car B LENGTHENS his lead over Car A, when Car B stops, Car A catches up a little bit, but because of the added time Car B got because of the time he spent in 45zone while car A was in 15 zone, i personally think Car B wins

ignore acceleration, obviously, they are going exactly the speed limit, why else would i have included it in there?anyway, ignore acceleration and decceleration

Answer 1

If it is assumed that both are at the same speed from time 0 and there is a lot of space so that they will be no accident....

They both arrive at the same time...
To cover the first 1/4 of the distance they will take same duration as speed limit is constant and there is no time for acceleration (=TTa = distance /15)

To cover the remaining 3/4 of the distance they will take same duration as speed limit is constant and there is no time for acceleration(=TTb = distance /45)

To stop for gas both of them will take same duration...(time G)

for 1st car
time = TTa/2 + G + TTa/2 + TTb
=TTa+TTb+G
for second
= TTa + TTb/2 + G + TTb/2
=TTa+TTb+G

Answer 2

assuming this is just another dumb oversimplistic and unrealistic school physics question, then the answer is either "neither", as they both finish at the same time (they've both travelled the same distance at the same speeds and stopped for the same amount of time), or "whichever car left first".

in reality i'd say the car that stopped for gas in the 15mph zone, as they'll end up driving past the second gas station at 45mph just as the other car is about to rejoin the highway; the driver of that second car will of course stop and wait for the first one to pass rather than pulling straight out and having an accident! assuming they don't get impatient and overtake or break the limit, and stay sat behind at a safe distance, they'll cross the line at least three seconds after the car that stopped early on.
(plus, as someone else mentioned, the stopping and restarting times in that ludicrously low speed limit are so much less than in the realistic one - effectively zero as you can reach that speed almost in the time it takes to floor the gas and release the brake, whereas 45 takes a few seconds longer both to reach and to comfortably stop from).

Answer 3

car a will arrive first, due to the fact that the speed that car a is travelling when it stops (15mph) as opposed to the speed (45mph) that car b is travelling.
If they stopped for 5 minutes, car a will lose 1.25 miles @ 15 mph, while car b continues on, gaining that same 1.25 miles. When car b stops for 5 minutes, it loses 3.75 miles @ 45 mph.
Car a will then make up the 1.25 miles it lost, and pick up 2.5 miles on car b, allowing car a to arrive first by about 3mins 33 secs.

How's that? Am I even close?

Stevo.

Answer 4

If there is no time loss in the acceleration and decceleration time going into and coming out of the gas station, then they arrive at the same time.

If accerleration and deceleration time counts, then car A arrive first.

Answer 5

we would want to discover the web % of automobile B = 60-50 =10 mph as automobile B travels 5m in the back of the motorized vehicle A so lets discover the time the motorized vehicle B overtakes automobile A with this % now S=vt or t=s/v= 5/10=a million/2 hours the time required to overhaul is 1/2 an hour

Answer 6

You gave speed limits not the speed at which each of the cars was travelling therefore it is impossible to give you an exact answer without making assumptions.

Answer 7

Car A wins.

Answer 8

It depends....What make are the cars? You get a ford and chevy..we all know which one will make it.The Chevy!!

Answer 9

they arrive at the same time:)

Answer 10

markp is somewhat cynical, but his analysis is correct.