James can jog twice as fast as he can walk. He was able to jog the first 9 miles to his grandmother’s house, but then he tired and walked the remaining 1.5 miles. If the total trip took 2 hours, then what was his average jogging speed?

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Answer 1 · 2018-06-12T00:36:06

James' jogging speed is 6 miles/hr

Let x miles/hr be the speed that James walks at
Then, 2x miles/hr is the speed that James runs at

If James runs for 9 miles, ie

#2x "miles" = 1 "hour"#
#9 "miles" = a "hour"# where a is a constant

#a=9/(2x)# hours

If James walks for 1.5 miles ie

#x "miles" = 1 "hour"#
#1.5 "miles" = b "hours"# where b is a constant

#b=1.5/x# hours

Since James travels for a total of 2 hours,

#1.5/x+9/(2x)=2#

#(3+9)/(2x)=2#

#6/x=2#

#x=3#

Hence, James walks for #3"miles"#/hr and runs for #6"miles"#/hr