8th grade math - Variations

Can you check the following, please?
1. Two minutes after a skydiver opens his parachute, he has descended 1900 feet. After 5 minutes, he descended 4750 feet. If distance varies directly with the time, at what rate is skydiver descending?

Ans: to find unit rate -1900/2 = 950
-4750/5 = -950
So, rate is -950 feet/minute.

2. Damon's earnings for four weeks from a part time job are shown in the table. Assume that his earnings vary directly with the number of hours worked. He can take a job that will pay him $7.35 per hour worked. Which job has the better pay?

Time worked: 15 12 22
Total Pay :112.50 90.00 165.00

Time worked: 9
Total Pay : 67.50

Ans: 112.50/15 = $7.50, 90/12 = $7.50, 67.50/9 = $7.50
So, current part job is better pay where $7.50 > $7.35.

3. A charter bus travels 210 miles in 3.5 hours. Assume the distance traveled is directly proportional to the time traveled. Write and solve a direct variation equation to find how far the bus will travel in 6 hours.

Ans: y = mx
210 = m(3.5)
210/3.5 = m
60 = m

y = 60*6hours
y = 360 miles in 6 hours

4. A monarch butterfly can fly 93 miles in 15 hours. Assume the distance traveled is directly proportional to the time traveled. Write and solve a direct variation equation to find how far the Monarch will travel in 24 hours.

Ans: y = mx
93 = 15m
93/15 = m
6.2 = m

y = 6.2(24hours)
y = 148.8 miles in 24 hours

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  1. #1, good
    #2. yes
    #3. yes
    #4. yes

    in #3, and #4 aren't you supposed to write the equation?

    y = 3.5x , where x is in hours, and y is miles

    and

    d = 6.2t , where t is in hours and d in miles

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  2. Thanks. Yes, I forgot about the equation.

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