I need help with math motion problems. Ex. Two cars left a shop. The first car travels 55 mph and left at 9:00 am. The other car left one hour later at 75 mph. At what time did the second car catch up with the first?
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and that'll be the number of hours after 9:00 AM. When we find out what ' T ' is,
we'll just count off that many hours after 9:00 AM and we'll have the answer.
-- The first car started out at 9:00 AM, and drove until the other one caught up
with him. So the first car drove for ' T ' hours.
The first car drove at 55 mph, so he covered ' 55T ' miles.
-- The second car started out 1 hour later, so he only drove for (T - 1) hours.
The second car drove at 75 mph, so he covered ' 75(T - 1) ' miles.
But they both left from the same shop, and they both met at the same place.
So they both traveled the same distance.
(Miles of Car-#1) = (miles of Car-#2)
55 T = 75 (T - 1)
Eliminate the parentheses on the right side"
55 T = 75 T - 75
Add 75 to each side:
55 T + 75 = 75 T
Subtract 55 T from each side:
75 = 20 T
Divide each side by 20 :
75/20 = T
3.75 = T
There you have it. They met 3.75 hours after 9:00 AM.
9:00 AM + 3.75 hours = 12:45 PM . . . just in time to stop for lunch together.
Also by the way ...
when the 2nd car caught up, they were 206.25 miles from the shop.
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Answer:
The answer is 96.
Step-by-step explanation:
Ok so all you have to do is list some multiples of each number.
32: 32, 64, 96, 128, 160, 192
48: 48, 96, 144, 192
As you can see, both numbers have the multiple 96, and that's the first one they have in common.
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A ratio given as p : q can be written as a fraction →
If we multiply the numerator and the denominator of the fraction with 2 or 3, fraction remains unchanged.
Following the same rule, ratio given as 3 : 11 can be written as,
Therefore. equivalent ratios to will be
and
.
Learn more,
When doing a ratio, its a comparison of numbers which often is was multiplied and then compared
So since you can't find a common factor above one to make it smaller, you have to multiply instead.
You can multiply each side by 3 and it would be 9:33 and it would be equivalent to
3:11 if you divide each side by 3
Other examples:
Multiplying each side by 5⇒ 15: 55
Multiplying each side by 10⇒30:110
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It's a factor. This concept is widely used throughout algebra, and you'll probably bump into it through the end of high school and beyond.
A common use is expressing a term in prime factorization, or reducing a number to its most base parts- primes. For example:
Of course, a number like 13 which is already prime is made up of itself and 1. Factors do not have to be primes. 20 is also reducible through combinations of 1, 2, 4, 5, 10, and 20. Prime factorization is just a handy example.
Basically, factors multiply with each other to create other numbers, and numbers can be reduced down to their factors.