# Math Help - How do I set up this problem?

1. ## How do I set up this problem?

A car travels at 60mph, a truck travels 55mph in the opposite direction. The vehicles pass in .34 seconds. How long is the truck?

How do I set this problem up??

2. ## Re: How do I set up this problem?

(60/3600+55/3600)*0.34*1609.344 = 17.479 meters

3. ## Re: How do I set up this problem?

60 mph = 88 ft/sec

55 mph = (242/3) ft/sec

rate of closure = 88 + (242/3) = (506/3) ft/sec

(rate)(time) = distance

(506/3 ft/sec)(34/100 sec) ... approx 57.35 ft

4. ## Re: How do I set up this problem?

Thanks to both of you, it is appreciated.

5. ## Re: How do I set up this problem?

The solutions above assume that the time it takes for the vehicles to pass is measured from the moment when their front bumpers align to the moment when the front bumper of the car aligns with the back of the truck. During this time, the car travels the whole truck's length relative to the truck. This is why the rate of closure times 0.34 s presumable equals the length of the truck. However, at the end of this time, the car and the truck still overlap. If we measure the passing time as the time when the vehicles overlap, then the rate of closure times 0.34 s equals the combined lengths of the vehicles.

6. ## Re: How do I set up this problem?

Hello, Ranger SVO!

A car travels at 60mph, a truck travels 55mph in the opposite direction.
The vehicles pass in 0.34 seconds. .How long is the truck?
Is that a misprint?

If this is conventional "passing vehicles", there is no unique solution.
. . We would need the length of the car.

Normally, the passing procedure begins when their front bumpers are even
. . and ends when their rear bumpers are even.

Code:
          * - - *
| car | →
* - - *
Start           * - - - - *
← |  truck  |
* - - - - *

* - - *
| car | →
End              * - - *
* - - - - *
← |  truck  |
* - - - - *
Let $C$ = length of the car.
Let $T$ = length of the truck.

They have a combined speed of $115$ mph.

It is as if the car has stopped
. . and the truck is passing at 115 mph.

The truck travels $5280(C+T)$ feet at $\tfrac{506}{3}$ ft/sec
. . and takes 0.34 seconds.

We have: . $5280(C+T) \:=\:\tfrac{506}{3}(0.34) \quad\Rightarrow\quad C+T \:=\:0.03258333$ feet.

The combined lengths of both vehicles is less than a half-inch!
And we still don't know the value of $T.$

7. ## Re: How do I set up this problem?

Originally Posted by Soroban
The truck travels $5280(C+T)$ feet at $\tfrac{506}{3}$ ft/sec
. . and takes 0.34 seconds.
Shouldn't this say, "The truck travels (C + T) feet at $\tfrac{506}{3}$ ft/sec and takes 0.34 seconds"?

8. ## Re: How do I set up this problem?

Answer keys are worthless if you can not work the problem, this problem is an example UIL calculator competition problem.

9. ## Re: How do I set up this problem?

Originally Posted by Ranger SVO