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Claire jogs 6 miles per hour and Megan jogs 5 miles per hour. They start together at their campsite and jog to an outpost 16 miles away. When Claire gets there, she immediately turns around and heads back towards Megan. How many miles will they be from the outpost when they meet? Express your answer as a mixed number.

 Oct 28, 2021
 #1
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At 6 m/hr   and 5 m/hr     when wil the total be 16 miles

 

Clair arrives at finish in 16/6 = 8/3 hr

Megan is at milepost  5 * 8/3 = 40/3 miles       with    16 - 40/3  miles to go =8/3 mile

closing speed then becomes 6+5 = 11 miles/hr

8/3 mile / 11 m/hr = 8/33 hr  to meet

16 -  8/33*6 = milepost = 14.55 miles from finish = .455 miles to go

 Oct 28, 2021
 #2
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Claire jogs 6 miles per hour and Megan jogs 5 miles per hour. They start together at their campsite and jog to an outpost 16 miles away. When Claire gets there, she immediately turns around and heads back towards Megan. How many miles will they be from the outpost when they meet? Express your answer as a mixed number.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The ratio of Claire's (C) speed to Megan's (M) speed is 6:5

 

C jogs 16 miles while M jogs 131/3 miles

 

The difference is 22/3 miles

 

(22/3 - M) / M = 6/5           M =  1 21/99

 

16 - (13 1/3 + 1 21/99) = 5/11     

 

Claire jogged 17 5/11 miles, while Megan jogged 'only' 14 6/11 miles.

 

(17 5/11 ) / (14 6/11 ) = 6 / 5

 Oct 28, 2021
edited by jugoslav  Oct 28, 2021
edited by jugoslav  Oct 28, 2021

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