(Solved) How do I set up this word problem as an algebraic expression (Not homework, practice book.)?

michaelW

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11 years ago

How do I set up this word problem as an algebraic expression (Not homework, practice book.)?

I'm trying to improve my math skills. Now I am in algebra, but I'm having trouble turning word problems into algebraic expressions. Anyway, here is the problem:

Two people start driving toward each other, starting from two towns 100 miles apart. If one person travels 30 miles per hour and the other person travels 20 miles per hour, how long will it take until they meet?

*You don't have to give me the answer, just set up the equation and explain what you did. Thanks

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bugz

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11 years ago

This verified answer contains over 110 words.

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riverfan

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11 years ago

Let t (in hours) be the amount of time it takes for the two people to meet.

Since distance = rate x time:
The first person travels a distance of 30 * t = 30t miles.
Similarly, the second person travels 20t miles.

Since the original gap between them is 100 miles, these distances must
add to 100 miles. In other words, 30t + 20t = 100.

I hope this helps!

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Rivalz93

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11 years ago

since both start at the same time they will travel the SAME amount of time to meet

use: time = distance /speed to find where the cars meet

let x represent the distance travelled by the faster car
for faster car: time = x/30

let (100 - x) represent the distance travelled by the slower car
for slower car: time = (100-x)/20

the times are equal

x/30 = (100 - x)/20
cross multiply

20x = 30(100 - x)
20x = 3000 - 30x
50x = 3000
x = 60
the faster car travels 60 miles to meet the slower car
since the faster car is travelling at 30 miles per hour this is 2 hours

I hope this helps

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smmoh4

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11 years ago

x = time (hours)
distance equals rate times time

distance traveled by person 1: 30x
distance traveled by person 2: 20x
total distance is 30x + 20x = 100
x = 2 hours

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juldina1

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11 years ago

1/2 hour

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lelas3

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11 years ago

No. of hours until they meet:
= 100/(30 + 20)
= 100/50
= 2

Answer: 2 hours

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