SOLUTION: A woman driving a car 14 ft long is passing a truck 30 ft long. The truck is traveling at 50 mi/h. How fast must the woman drive her car so that she can pass the truck completely i

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Question 158128This question is from textbook Algebra and trigonometry
: A woman driving a car 14 ft long is passing a truck 30 ft long. The truck is traveling at 50 mi/h. How fast must the woman drive her car so that she can pass the truck completely in 6 s, from the position shown in figure (A) to the position shown in figure (B)?
(A)
---CARI --->
---------I
---------IT-R-U-C-K -->
---------I
(B)
-------------I
-------------ICAR -->
-------------I
T-R-U-C-KI --->
This question is from textbook Algebra and trigonometry

Found 2 solutions by Edwin McCravy, cattycassie77:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
A woman driving a car 14 ft long is passing a truck 30 ft long. The truck is traveling at 50 mi/h. How fast must the woman drive her car so that she can pass the truck completely in 6 s, from the position shown in figure (A) to the position shown in figure (B)?

She would really have to be flying to pass that truck in
only 6 seconds.

First we must change 50 mi/h to ft/s.

%2850mi%29%2F%281h%29

replace mi by 5280ft
replace 1h by 60min

%2850%285280ft%29%29%2F%2860min%29

replace min by 60s

%2850%285280ft%29%29%2F%2860%2860s%29%29

264000ft%2F%283600s%29

%28220ft%29%2F%283s%29

So in 6 seconds, using d=rt,
the truck travels

d=rt=%28%28220ft%29%2F%283s%29%29%286s%29=+440ft

We start with the front bumper of the car even
with the tailgate of the truck.

So in that 6 seconds, the front bumper of the 
car must travel:

1. the 440 feet which the truck travels in 6 seconds.
2. the 30 feet from the tailgate of the
   truck to the front bumper of the truck.
3. the 14 feet to get the back bumper of
   the car even with the front bumper of the
   truck.

That's a total of 440%2B30%2B14=484feet, which she
must travel in 6 second.  

Now we find her rate using r=d%2Ft

r=%28484ft%29%2F%286s%29
r=%28484ft%29%2F%286s%29
r=%28242ft%29%2F%283s%29
r=%28242ft%29%2F%283s%29

Now we must get that to mi%2Fh:

Multiply by %281mi%29%2F%285280ft%29

r=%28242ft%29%2F%283s%29×%281mi%29%2F%285280ft%29

Multiply by 60s%2F1min

r=%28242ft%29%2F%283s%29×%281mi%29%2F%285280ft%29×60s%2F1min

Multiply by %2860min%29%2F%281hr%29

r=%28242ft%29%2F%283s%29×%281mi%29%2F%285280ft%29×60s%2F1min×%2860min%29%2F%281hr%29

Cancel the ft, the s, and the min:

r=%28242cross%28ft%29%29%2F%283cross%28s%29%29×%281mi%29%2F%285280cross%28ft%29%29×60cross%28s%29%2F1cross%28min%29×%2860cross%28min%29%29%2F%281hr%29

r=165mi%2Fh

That's fast!!!  I don't she'll do it, do you?

Edwin

Answer by cattycassie77(2) About Me  (Show Source):
You can put this solution on YOUR website!
264,000 per hour
264000ft/3600 sec
(264,000/3600)=(x/6)
x=440 feet+16+30=484 ft/6sec
290400ft/3600 sec
55 miles per hour