SOLUTION: Phil leaves Northampton and walks north for an hour and a half. Don leaves Northampton
at the same time and rides his bicycle south at a rate of 10 mph. Phil stops walking and
Do
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at the same time and rides his bicycle south at a rate of 10 mph. Phil stops walking and
Do
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Question 1194181: Phil leaves Northampton and walks north for an hour and a half. Don leaves Northampton
at the same time and rides his bicycle south at a rate of 10 mph. Phil stops walking and
Don continues to bike for another half an hour. At the end of the excursion, they find
themselves 26 miles apart. What is Phil's rate? Found 2 solutions by ikleyn, math_tutor2020:Answer by ikleyn(52784) (Show Source):
You can put this solution on YOUR website! .
Phil leaves Northampton and walks north for an hour and a half. Don leaves Northampton
at the same time and rides his bicycle south at a rate of 10 mph. Phil stops walking and
Don continues to bike for another half an hour. At the end of the excursion, they find
themselves 26 miles apart. What is Phil's rate?
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Don biked two hours and covered 2*10 = 20 miles south.
Hence, Phil moved 26-20 = 6 miles north.
Phil spent 1.5 hours, hence Phil' rate was = 4 miles per hour. ANSWER
You can put this solution on YOUR website!
The ultimate question here is "What is Phil's rate?"
So we'll let x be the this unknown value
x = Phil's rate or speed in mph
This is some positive real number.
Use the formula
distance = rate*time
to find this equation for Phil
d = r*t
d = x*1.5
d = 1.5x
After 1.5 hours (aka an hour and a half), Phil has walked 1.5x miles.
Meanwhile, Don travels at a rate of 10 mph and started traveling south at the same time Phil went north.
Don travels for the 1.5 hours mentioned, but an extra 1/2 = 0.5 an hour to get a total of 1.5+0.5 = 2 hours of travel.
Let's find how far Don traveled south:
d = r*t
d = 10*2
d = 20
Don traveled 20 miles south.
Add this onto the 1.5x miles Phil traveled north. Then set this to the 26 mile gap between the two people.
It might help to draw out a vertical number line.
1.5x+20 = 26
1.5x = 26-20
1.5x = 6
x = 6/(1.5)
x = 4
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