John and Susan leave a neighborhood restaurant after having

John and Susan leave a neighborhood restaurant after having dinner. They each walk to their respective homes. John’s home is 3120 feet due north of the restaurant and Susan’s home is 2018 feet due south of the restaurant. John leaves at 7:30 pm traveling at a constant speed of 334 feet per minute and Susan leaves at 7:30 pm traveling at a constant speed of 219 feet per minute.

diagram A represents this situation at 7:31 pm

A) At 7:31 pm what is the distance (in feet) between John and Susan?

B) For every minute that elapses what is the change in the distance between John and Susan?

C) Write a formula that gives the distance between John and Susan, dd, in terms of the number of minutes that have elapsed, tt, since they left the restaurant.

D) How many seconds will the person who gets home first be home before the other person gets home?

3120 feet 3120 feet 2018 feet 2018 feet Susan\'s house John\'s house John\'s house Susans Susan\'s house restaurant 219 feet 334 feet 3120 feet 3120 feet 2018 feet 2018 feet John\'s house Susan\'s house Johns house John\'s Susan\'s house restaurant 219.feet 334 feet

Solution

Ans(A):

at 7:31 pm means time of travel = 1 minute as they started walking at 7:30 pm

speed of Jhon = 334 feet per minute

distance covered by Jhon in 1 minute =334 feet

speed of Susan = 219 feet per minute

distance covered by Susan in 1 minute =219 feet

Hence distance between both = 334+219 =553 feet ( I added them not subtracted because both are going in opposite directin North and South)

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Ans(B):

For every minute that elapses, change in the distance between John and Susan will be fixed to 553 feet because they are going in exactly opposite directions with fixed speed.

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Ans(C):

distance covered by Jhon in t minutes =334t feet

distance covered by Susan in t minutes =219t feet

Hence distance between both after t minutes elapsed= 334t+219t =553t feet

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Ans(D):

John’s home is 3120 feet

speed of Jhon = 334 feet per minute

time taken by Jhon to reach home = distance/time= 3120/334 minutes= (3120/334)*60 seconds=560.48 seconds.

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Susan’s home is 2018 feet

speed of Susan= 219 feet per minute

time taken by Jhon to reach home = distance/time= 2018/219 minutes.=( 2018/219)*60 seconds=552.88 seconds

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Hence number of seconds taken by the person who gets home first before the other person gets home=560.48 -552.88 =7.6 seconds