Nancy and mark commute to work, traveling in opposite directions. nancy leaves the house at 7: 00 a. m. and average 20 miles per hour. mark leaves at 7: 15 a. m. and averages 40 miles per hour. at what time will they be 170 miles apart?

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

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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