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# Algebra problem

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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 60 minutes at 3 miles an hour. He then waited 10 minutes forgrandma, and once she caught up, they finished the hike (at her pace) in 30 minutes.What was the total distance of the hike in miles? Please give the answer rounded to the nearest tenth of a mile.

Jun 3, 2022

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4 mph x 20/60 ==1 1/3 miles that Tony hiked in the first 20 minutes.

3 mph x 60/60==3.00 miles that Tony hiked in the following 60 minutes.

[20 + 60 + 10] / 60==1.5 - hours that Tony spent hiking and resting ahead of grandma.

[1 1/3 + 3 ]==4 1/3 miles that Tony hiked ahead of grandma.

4 1/3 / 1.5 ==2 8/9 mph - grandma hiking speed.

[2 8/9 * 1/2] + [2 8/9 * 1/2] ==2 8/9 miles that grandma hiked in the first 30 minutes + the last 30 minutes.

2 8/9  +  4 1/3 ==65 / 9 ==7 2/9 miles - total distance that Tony and grandma hiked together.

Jun 3, 2022