Joe and Theresa want to paint their living room. From past experience they know that Joe can paint the room in 6 hours and Theresa can paint it in 10 hours. How long will it take them if they work together?
Mower A can cut a field in 6 hours and Mower B cut the same field in 2 hours. How long would it take both mowers working together to cut the field.
A certain amount of money is invested for one year at 8% simple intrest. The total principal and intrest at the end of the year is $1620. Find the original amount invested.
I have trouble with setting up word problem equations. If you could just help me set up the equation im sure I could solve and get the right answer.
Joe does 1/6 room/hour
Theresa does 1/10 room per hour
together they do (1/6+1/10) = 5/30 + 3/30 = 8/30 = 4/15 of a room /hour
so 15/4 hours/room (about 4 hours)
same deal with the mowers
1/6 + 1/2 = 1/t
2/3 = 1/t
t = 1.5
1.08 x = 1620
Thank you so much I really appreciate you helping me set up these problems, again thank you!
You are welcome :)
Sure, I can help you set up the equations for these word problems.
1) Let's denote the time it takes for them to paint the room together as "t". Joe can paint the room in 6 hours, so his painting rate is 1/6 of the room per hour. Similarly, Theresa can paint the room in 10 hours, so her painting rate is 1/10 of the room per hour. When they work together, their rates add up, so the equation is:
(1/6 + 1/10) * t = 1
This equation is derived from the fact that the combined rate of painting is equal to 1 room per t hours.
2) Mower A can cut the field in 6 hours, so its cutting rate is 1/6 of the field per hour. Mower B can cut the same field in 2 hours, so its cutting rate is 1/2 of the field per hour. When they work together, their rates add up, so the equation is:
(1/6 + 1/2) * t = 1
This equation is derived from the fact that the combined rate of cutting is equal to 1 field per t hours.
3) Let's denote the original amount invested as "x". The interest earned in one year can be calculated using the formula: Interest = Principal * Rate * Time, where the rate is given as 8% or 0.08 and the time is 1 year. Therefore, the interest earned is 0.08 * x * 1 = 0.08x. The total principal and interest at the end of the year is given as $1620, so the equation is:
Principal + Interest = $1620
x + 0.08x = $1620
This equation is derived from the fact that the sum of the original amount invested and the interest earned is equal to $1620.