Susan, Lisa and Rodger are all travelling due west at constant speed, and have b
ID: 1941118 • Letter: S
Question
Susan, Lisa and Rodger are all travelling due west at constant speed, and have beendoing so for a while. Susan is driving 60 miles per hour and is 60 miles due west of
Manhattan. Lisa is running at 10 miles per hour is 22.5 miles west of Manhattan.
Rodger is riding a bicycle at 20 miles per hour and is 30 miles due west of Manhattan.
Could they all have started from the same place at the same time? When and where?
I understand the question but I'm not sure where to start in tacking it. Any help is greatly appreciated. Thanks!
Explanation / Answer
Begin by looking at how long each has been traveling since they reached Manhattan. Susan: 60mph and 60 miles west of Manhattan means she was in Manhattan 1 hour ago. Lisa: 10mph and 22.5 miles west of Manhattan means she was in Manhattan 2.25 hours ago. Rodger: 20mph and 30 miles west of Manhattan means he was in Manhattan 1.5 hours ago. The fact that they were going through Manhattan is largely irrelevant; what really matters is that the location gives us a perspective. This gives us a point from which we can derive a system of equations between all 3 people. We have: (distance to Manhattan for Susan)/(Susan's speed) + 1 hour = (distance to Manhattan for Lisa)/(Lisa's speed) + 2.25 hours = (distance to Manhattan for Rodger)/(Rodger's speed) + 1.5 hours Plugging in the known variables for any 2 of the equations in this equality allows us to solve for the distance due east of Manhattan for all 3 of them to have started at the same place and at the same time. Doing so will produce the result "-15" which means they were all 15 miles West of Manhattan already when they started. 6d miles / 60 mph [Lisa] = d miles / 60 mph [Susan] => d = -15 miles Since no specific time is given, we respond with "time before now" which corresponds to the amount of time that has elapsed since they all ended up where they are in the context of the problem. All 3 answers should line up: Susan: 1 hour - 15 miles / 60 mph = 1 hour - .25 hours = .75 hours Lisa: 2.25 hours - 15 miles / 10 mph = 2.25 hours - 1.5 hours = .75 hours Rodger: 1.5 hours - 15 miles / 20 mph = 1.5 hours - .75 hours = .75 hours Therefore, they all started 15 miles west of Manhattan exactly 3/4 of an hour before this problem was posed.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.