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zaharov [31]
3 years ago
12

Nancy and Mark commute to work, traveling in opposite directions. Nancy leaves the house at 7:00 A.M. And average 20 miles per h

our. Mark leaves at 7:15 A.M. And averages 40 miles per hour. At what time will they be 170 miles apart?
Mathematics
1 answer:
vladimir2022 [97]3 years ago
4 0

Answer:

They will be 170 miles apart at 10 AM

Step-by-step explanation:

Nancy has 15´ of  head start which is 1/4 hr.

NHD = 20*(1/4) = 5 miles is her head start

Mark leaves at 7.15hs = starting point

Marks stop at when they are 170 miles apart = t

------------------------------

t = the time they are 170 miles apart

d= distance in miles Nancy travels in time t

170 - (d+5) = distance in miles Mark travels in time t

------------------------------

Nancy's equation:

(1) d = 20t

Mark's equation:

(2) 170 - (d+5) = 40t

---------------------------

(2) 170-d-5=40t

(2) d+40t=165

Substitute (1) into (2)

(2) 20t+40t=165

(2) 60t=165

(2) t=2.75

7:15 AM + 2.75 hrs (2:45hs) = 10 AM

They are 170 miles apart at 10 AM

check:

(1) d=20t

(1) d=20*2.75

(1) d= 55

---------------

(2) 170 - (d+5) = 40t

(2) 170 - (d+5) = 40*2.75

(2) 170 - d-5 = 110

(2) d=55

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Find the following rates. Round your answer to the nearest hundredth. a. ? % of 75 = 5 b. ? % of 28 = 140 c. ? % of 100 = 40 d.
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Answer:

a) 6.67% b) 500% c) 40% d) 7.5%

Step-by-step explanation:

a. ? % of 75 = 5

<em>Let ? be y.</em>

<em>Of means multiply so we will replace it with a multiplication sign.</em>

<em>y% x 75 = 5</em>

<em>y% = 5/75</em>

<em>y% = 1/15 x 100</em>

y = 6.67 %

b) ?% of 28 = 140

<em>Let ? be y.</em>

<em>Of means multiply so we will replace it with a multiplication sign.</em>

<em>y% x 28 = 140</em>

<em>y% = 140/28</em>

<em>y% = 5</em>

<em>y = 5 x 100</em>

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c) ?% of 100 = 40

<em>Let ? be y.</em>

<em>Of means multiply so we will replace it with a multiplication sign.</em>

<em>y% x 100 = 40</em>

<em>y% = 40/100</em>

<em>y% = 2/5</em>

<em>y = 2/5 x 100</em>

y = 40%

d) ?% of 200 = 15

<em>Let ? be y.</em>

<em>Of means multiply so we will replace it with a multiplication sign.</em>

<em>y% x 200 = 15</em>

<em>y% = 15/200</em>

<em>y% = 3/40</em>

<em>y = 3/40 x 100</em>

y = 7.5 %

!!

8 0
3 years ago
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