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Tony and his grandma went hiking together. Grandma was slow but steady and maintained the same speed throughout. Tony accompanied grandma at her pace forthe first 30 minutes. Then he walked ahead for the next 20 minutes at 4 miles an hour. And the next 40 minutes at 3 miles an hour. He then waited 15 minutes forgrandma, and once she caught up, they finished the hike (at her pace) in 20 minutes.What was the total distance of the hike in miles? Please give the answer rounded to the nearest tenth of a mile.

 Jan 23, 2021
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Tony and his grandma went hiking together. Grandma was slow but steady and maintained the same speed throughout. Tony accompanied grandma at her pace forthe first 30 minutes. Then he walked ahead for the next 20 minutes at 4 miles an hour. And the next 40 minutes at 3 miles an hour. He then waited 15 minutes forgrandma, and once she caught up, they finished the hike (at her pace) in 20 minutes.What was the total distance of the hike in miles? Please give the answer rounded to the nearest tenth of a mile.

 

Mmmm......this one  looks  interesting...

 

30min = 1/2  hr

20 min = 1/3 hr

40 min = 2/3 hr

15 min = 1/4 hr

 

Call Gramdma's  pace =  P 

 

For the first  part of the  hike, the  distance  covered  =  (1/2)hr * P

 

For  the next part of the  hike  the distance that  grandma covers is grandma covers  =

(Tony's  time  hiked  when he walked alone + time he waited ) P  = 

( 1/3 hr + 2/3 hr + 1/4 hr) P

And this  equals the  distance that  Tony covers  =  ( 1/3)hr *4 + (2/3)hr *3  =  10/3 miles

 

So

 

10/3  = ( 1/3 + 2/3 + 1/4) P

10/3   =  ( 1 + 1/4) P

(10/3) = (5/4) P

P = (10/3) ( 4/5)  =  40/15 =  8/3  mi/hr

 

So   the total distance  hiked =   

 

(1/2)(8/3)  +  10/3  +  (1/3)(8/3)   = 

 

4/3  + 10/3  + 8/9  =

 

14/3 +  8/9  =

 

[42 + 8 ]  /  9  =

 

50/9  miles ≈  5.55 miles  =  5.6 miles 

 

 

cool cool cool

 Jan 23, 2021

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