If it takes one person 4 hours to paint a room and another person 12 hours to
paint the same room, working together they could paint the room even quicker, it
turns out they would paint the room in 3 hours together. This can be reasoned by
the following logic, if the first person paints the room in 4 hours, she paints 14 of
the room each hour. If the second person takes 12 hours to paint the room, he
paints 1 of the room each hour. So together, each hour they paint 1 + 1 of the 12 4 12
room. Using a common denominator of 12 gives: 3 + 1 = 4 = 1. This means 12 12 12 3
each hour, working together they complete 13 of the room. If 13 is completed each hour, it follows that it will take 3 hours to complete the entire room.
This pattern is used to solve teamwork problems. If the first person does a job in A, a second person does a job in B, and together they can do a job in T (total). We can use the team work equation.
Teamwork Equation: A1 + B1 = T1
Often these problems will involve fractions. Rather than thinking of the first frac-
tion as A1 , it may be better to think of it as the reciprocal of A’s time.
World View Note: When the Egyptians, who were the first to work with frac- tions, wrote fractions, they were all unit fractions (numerator of one). They only used these type of fractions for about 2000 years! Some believe that this cumber- some style of using fractions was used for so long out of tradition, others believe the Egyptians had a way of thinking about and working with fractions that has been completely lost in history.
Answer:
6 gallons
Step-by-step explanation:
You can find this using the ration method.
If, 8 gallons : 192 miles
x gallons : 144 miles
We must find the value of x, which is the number of gallons used to travel 144 miles.
Cross multiply the ratios.
192 x = 8 × 144
192 x = 1152
x = 1152 ÷ 192
x = 6
∴ It takes 6 gallons to travel 144 miles.
(x-3)2+(y-4)2=24
2x-6+2y=24
2x-14+2y=24
2x=24+14-2y
2x=38-2y
x=19-y
Answer:
The middle between two numbers is the average of those numbers. So we add those two numbers together and divide by two. And the answer is (1 + 6) / 2 = 3.5
