SOLUTION: Cars traveling at 120 km/h on a highway to Florida during the march break are separated, on the average, by only 5 m. There are 1000 cars on a straight stretch of the highway. If e

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Question 1200034: Cars traveling at 120 km/h on a highway to Florida during the march break are separated, on the average, by only 5 m. There are 1000 cars on a straight stretch of the highway. If each car averages 3.5m in length how far is it from the back of the last car to the front of the first car?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

We start off with one car. It will be placed to the very left, and it's be the last car in the chain.
We start off with 3.5 meters in total length.

Then add on a second car. Place it to the right of the initial car.
We add on the 5 meter gap and the 3.5 meter car length to get a total addition of 5+3.5 = 8.5 meters.
Each time we add on a new car to the right, we'll add on 8.5 meters.

There will be 1000-1 = 999 new additions to be placed to the right of the initial car.
999*8.5 = 8491.5 meters is the added distance
Add that onto the initial car length 3.5 meters to get 8491.5 + 3.5 = 8495 meters = 8.495 kilometers
Divide by 1000 to go from meters to kilometers (i.e. move the decimal point 3 spots to the left).

Answer: 8.495 km
This value is an approximation because the gap between cars (5 m) and the car lengths (3.5 m) are average approximations.

Side note: 8.495 km = 5.2785 miles approximately

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Another approach:

There are 1000 cars and 1000-1 = 999 gaps
999 gaps lead to 999*5 = 4995 meters of empty road

1000 cars = 1000*3.5 = 3500 meters if the cars were touching end to end

Of course they aren't touching and we have to add in the gaps
3500+4995 = 8495 meters = 8.495 kilometers

Answer: 8.495 km

Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let the number of cars be n; then the number of separating gaps is (n-1).


Then the answer to the problem's question is this expression 3.5n + 5(n-1).


Since n= 1000,  this distance is  3.5*1000 + 5*999 = 8495 meters.    ANSWER


The same as 3.5*1000 + 5*1000 - 5 = 8.5*1000 - 5 = 8500 - 5 = 8495 meters,

so it can be computed mentally.

Solved.