+328 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.
+129852 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
