Let the daily played number of pop songs be P, the number of rock songs be R and the number of hip-hop songs be H.
i)
"A radio station plays a total of 272 pop, rock, and hip-hop songs during a day"
means that : P+R+H=272
ii)
"The number of pop songs is 3 times the number of rock songs. "
so, P=3R
iii)
"The number of hip-hop songs is 32 more than the number of rock songs."
means: H=32+R
iv)
since both P and H can be written in terms of R, we have:
P+R+H=272
(3R)+R+(32+R)=272
3R+R+32+R=272
5R+32=272
5R=272-32=240
R=240/5=48
vi)
thus: P=3R=3*48=144, H=32+R= 32+48=80
Answer:
48 Rock, 144 Pop and 80 Hip-hop
Beth's speed was 60 mph.
<h3>
What is speed?</h3>
- The speed (commonly referred to as v) of an object in everyday use and kinematics is the magnitude of the change in its position over time or the magnitude of the change in its position per unit of time; it is thus a scalar quantity.
- The distance traveled by an object in a time interval is divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero.
- Velocity is not the same as speed.
To find what was Beth's speed:
Beth's data:
- time = 2 hrs; rate = r mph; distance = r×t = 2r miles
Tim's data:
- time = 1 hr; rate = r-6 mph; distance = r-6 miles
Equation:
- distance + distance = 174 miles
So,
- 2r + r - 6 = 174
- 3r - 6 = 174
- 3r = 180
- r = 60 mph (Beth's rate)
- r-6 = 54 mph (Tims's rate)
Therefore, Beth's speed was 60 mph.
Know more about speed here:
brainly.com/question/4931057
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Can i have brainlist i will love you for the rest of my life