algebra word problem help needed?

Question

woman driving a car 14ft long is passing a truck 30 ft long. the truck is traveling 50 mi/h. she wants to completely pass the truck in 6 seconds. assume that they are in parallel lanes traveling the same direction and her front bumper is currently even with the trucks rear bumper. she wants to finish with her rear bumper past his front bumper.
I worked this repeatedly and could not build a proper equation. I understand d = r * t, that she is going to travel 58 ft in 6 seconds, and she has to go 50 + x mph to pass the truck. I'm stumped otherwise.

Answer 1

So part of the problem is, you're trying to deal with distance, but you have two different units. First, you need to calculate how many feet are in a mile. I did this simply by googling a unit converter, and got that 1 mile = 5280 feet. Therefore, in feet per second, the truck is going (50)(5280), or 264000 ft/h. Now, to get that into seconds, divide 264000 by (60)(60) (getting it from ft/hr to ft/min then ft/s):
73.333 ft/s

Now, in order to pass him, her speed must be greater than 73.333 ft/s, plus the additional bit to make sure she is past him. His car is 30 feet, her's is 14, so since she lines up along his back bumper with her front bumper, she must go 14 feet to be aligned back bumper to back bumper, then must go an additional 30 feet to make sure her back bumper is past his front bumper.

Therefore, she must travel 44 feet in six seconds, or 7.333 ft/s.

Hence, the inital speed, 73.333, + the required additional speed to pass 44 ft in six seconds, 7.333 ft/s, gives you

80.666 ft/s. If need be, convert this back to miles per hour:

80.666 ft/s * (60)(60) = 290397.6 ft/hr

290397 / 5280 = 54.999 mi/hr, or simply 55

Hopefully that helps

Answer 2

First off, she only needs to go 30 + 14 = 44 feet farther than the truck goes in 6 seconds. You can convert 50 mph to feet per sec by multiplying by 5280 (feet in a mile)then dividing by 3600 (sec in an hour). That comes out 73 1/3 feet per second, times 6 seconds is 440 feet, which id how far the truck goes in those six seconds (like you said, d = r * t). So she must drive 440 + 44 = 484 feet in 6 seconds or 80 2/3 ft/sec

Convert this back to miles per hour by doing the opposite of the other conversion. It comes out 55 mph.

Answer 3

How fast does she have to go in order for her vehicle to travel 44 feet farther than his truck goes? She has to travel 30 feet to catch up to him, then go 14 more to pass him. Plus whatever mileage he travels, she must do that, too.

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IOW, if he travels x miles in 6 seconds, she must travel (x miles + 44 feet) in 6 seconds.

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One more way to explain it.

In 6 seconds, she must travel the distance he travels, plus 30 feet to catch up with him, plus 14 feet to clear his vehicle.


123 567 901 34~123 5678 0123 5678 0123 567 90

Pretend the left number is her car, and the number on the right of the wavy line is the truck. If he were standing still, she woule have to go 30 feet to catch up, then 14 more to pass him. But, she also has to travel the distance he traveled.

I had to put spaces where some numbers go, otherwise Yahoo puts dashes at the end and cuts off half the number. I tried to demonstrate. Didn't work like I hoped.


He travels 5 miles in 6 seconds. So she has to travel 5 miles plus 44 feet in 6 seconds. That's easy to do. Convert to feet. Sorry I'm slow. This is NOT the best answer. LOL! I must have not gotten enough sleep last night.

..

Answer 4

First you need to convert MPH to feet and seconds.

50mph = 264,000 feet per 3,600 seconds, or 73.333333333 feet per second.

In order for her to completely pass the truck, she needs to travel 58 feet. I'm going to assume she wants to pass the truck within 6 seconds since you didn't explain it very well. In which case, she needs to drive roughly 298,800 feet per 3600 seconds. Now it just needs to be converted back to MPH, which would be about 56.6mi/h.

Answer 5

The answer is : r* 4 + 16 = 57 divided by is 24.5 mph that she passed the truck !

Answer 6

You have the answer just perform a unit conversion on it.
But, shouldn't it be 44 ft in 6 seconds?

44 ft (1 mile)(60 sec)(60 min)
-------------------------------------------- = 5 mph
6 sec(5280 ft)(1 min) (1 hr)

so 55 mph