I need help with two problems to finish my assignment. #1 The length of a rectangle is fixed at 29cm. What widths will make the perimeter greater than 86 cm? If I could get the equation for this I would be able to figure it.
I saw this one posted and no response yet. #2 Trains A and B are traveling in the same direction. Train A is traveling at 100 mph and Train b is traveling at 110 mph. Train A passed a station at 1:15 pm and Train B passed the same station at 1:45pm. At what time will Train B catch up with Train A?
first one:
let the width be w
remember P = 2(l+w)
so 2w + 58 > 86
etc.
for two:
let the time from the moment that train B passed the station to the moment it passes train A be t hours.
distance travelled by A since 1:45 pm is (50 + 100t)
(Distance = rate x time, so the 50 is the distance A went from 1:15 to 1:45, which was 1/2 hour)
distance traveled by B since 1:45 is 110t
so 110t = 50 + 100t
10t = 50
t = 5
so 5 hours from 1:45 pm or 6:45 pm
how can i graph the inequality 4x+5y is greater than or equal to 20 in a plane?
#2 Please help to graph the system of inequalities y is less than or equal to -5 and x is less than or equal to 6 just finishing up an assignment thnaks
Thanks Reiny
Sure, let's break down both problems one by one.
Problem #1:
To find the equation for the perimeter of a rectangle, we need to know the formulas involved. For a rectangle, the perimeter (P) is equal to two times the sum of its length (L) and width (W):
P = 2(L + W)
In this case, we are given that the length (L) is fixed at 29 cm, and we want to find the widths (W) that make the perimeter greater than 86 cm. So, we can rewrite the equation as:
86 < 2(29 + W)
Let's simplify this equation further:
86 < 58 + 2W
Subtracting 58 from both sides:
28 < 2W
Now, we can divide both sides by 2:
14 < W
Therefore, the widths (W) that make the perimeter of the rectangle greater than 86 cm are any values larger than 14 cm.
Problem #2:
To solve this problem, we need to determine the time it takes for Train B to catch up with Train A. Since Train A started 30 minutes earlier than Train B (1:15 pm - 1:45 pm), we can calculate this time difference.
Let's denote the time it takes for Train B to catch up as "t" (in hours). We also know that Train A is traveling at 100 mph and Train B at 110 mph.
To find the equation representing the distance traveled by each train, we can use the formula:
Distance = Speed x Time
For Train A: Distance_A = 100t
For Train B: Distance_B = 110(t - 0.5) (since it started 0.5 hours later)
As Train B catches up with Train A, the distance traveled by both trains will be equal:
100t = 110(t - 0.5)
Simplifying the equation:
100t = 110t - 55
55 = 10t
t = 55/10 = 5.5
Therefore, Train B will catch up with Train A after 5.5 hours.
To determine the time at which this occurs, we need to add the catch-up time to the starting time of Train A:
1:15 pm + 5.5 hours = 6:45 pm
Train B will catch up with Train A at 6:45 pm.
I hope this helps! Let me know if you have any further questions.