- Sara: 148 miles
- Eli: 74 miles
- Ashley: 222 miles
- Hazel: 444 miles
Further explanation
Given:
- Sara travels twice as far as Eli when going to camp.
- Ashley travels as far as Sara and Eli together.
- Hazel travels three times as far as Sara.
- In total, all four travel a total of 888 miles to camp.
Question:
How far does each of them travel?
The Process:
From these four people, we start from Eli.
Let's call Eli's travel as d.
[tex]\boxed{ \ Eli's \ travel = d \ }[/tex]
Sara travels twice as far as Eli.
[tex]\boxed{ \ Sara's \ travel = 2d \ }[/tex]
Ashley travels as far as Sara and Eli together.
[tex]\boxed{ \ Ashley's \ travel = d + 2d \rightarrow \boxed{ \ Ashley's \ travel = 3d \ }}[/tex]
Hazel travels three times as far as Sara.
[tex]\boxed{ \ Hazel's \ travel = 3 \times 2d \rightarrow \boxed{ \ Hazel's \ travel = 6d \ }}[/tex]
In total, all four travel a total of 888 miles to camp.
[tex]\boxed{ \ d + 2d + 3d + 6d = 888 \ }[/tex]
[tex]\boxed{ \ 12d = 888 \ }[/tex]
[tex]\boxed{ \ 12 \times d = 888 \ }[/tex]
[tex]\boxed{ \ d = 888 \div 12 \ }[/tex]
[tex]\boxed{\boxed{ \ d = 74 \ }}[/tex]
We have obtained d. The final step is to substitute the value of d for each person's travel.
- [tex]\boxed{ \ Eli's \ travel = d \rightarrow \boxed{ \ Eli's \ travel = 74 \ miles \ }}[/tex]
- [tex]\boxed{ \ Sara's \ travel = 2d \rightarrow \boxed{ \ Sara's \ travel = 2 \times 74 = 148 \ miles \ }}[/tex]
- [tex]\boxed{ \ Ashley's \ travel = 3d \rightarrow \boxed{ \ Ashley's \ travel = 3 \times 74 = 222 \ miles \ }}[/tex]
- [tex]\boxed{ \ Hazel's \ travel = 6d \rightarrow \boxed{ \ Hazel's \ travel = 6 \times 74 = 444 \ miles \ }}[/tex]
Thus we already know how far each of them travels.
- - - - - - -
The summary scheme is as follows:
- Eli's travel ⇒ [tex]\boxed{d}[/tex]
- Sara's travel ⇒ [tex]\boxed{d}\boxed{d}[/tex]
- Ashley's travel ⇒ [tex]\boxed{d}\boxed{d}\boxed{d}[/tex]
- Hazel's travel ⇒ [tex]\boxed{d}\boxed{d}\boxed{d}\boxed{d}\boxed{d}\boxed{d}[/tex]
[tex]\boxed{d}\boxed{d}\boxed{d}\boxed{d}\boxed{d}\boxed{d}\boxed{d}\boxed{d}\boxed{d}\boxed{d}\boxed{d}\boxed{d} = 888[/tex]
[tex]\boxed{ \ 12 \times d = 888 \ }[/tex]
[tex]\boxed{ \ d = 888 \div 12 \ }[/tex]
[tex]\boxed{\boxed{ \ d = 74 \ }}[/tex]
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Keywords: Sara travels, twice, as far as, Eli, when going to camp, Ashley, Hazel, three times, In total, all four travel, 888 miles, how far, each, substitute
