Devin throws a football 7 and 1/3 yards. Carl throws it 2 and 1/2 times farther. How many yards does Carl’s throw more travel than Devin’s?
11 yards.
\(2 \frac{\mathrm{1} }{\mathrm{2}} \) yards.
\(7 \frac{\mathrm{1} }{\mathrm{3}} \) yards.
\(18 \frac{\mathrm{1} }{\mathrm{3}} \) yards.
Detailed Explanation
Carl's throw went: \(7 \frac{\mathrm{1} }{\mathrm{3}} × 2 \frac{\mathrm{1} }{\mathrm{2}} = \frac{\mathrm{22} }{\mathrm{3}} × \frac{\mathrm{5} }{\mathrm{2}} = \frac{\mathrm{110} }{\mathrm{6}} = 18 \frac{\mathrm{1} }{\mathrm{3}}\)
The difference between the two throws is: \(18 \frac{\mathrm{1} }{\mathrm{3}} - 7 \frac{\mathrm{1} }{\mathrm{3}}\)
To subtract these, you need to find a common denominator, which is 3 in this case: \(18 \frac{\mathrm{1} }{\mathrm{3}} - 7 \frac{\mathrm{1} }{\mathrm{3}} = \frac{\mathrm{54} }{\mathrm{3}} + \frac{\mathrm{1} }{\mathrm{3}} - \frac{\mathrm{21} }{\mathrm{3}} - \frac{\mathrm{1} }{\mathrm{3}}\)
Now, combine the fractions: \(\frac{\mathrm{54 + 1 -21-1} }{\mathrm{3}} = \frac{\mathrm{33} }{\mathrm{3}} = 11\)
Carl's throw traveled 11 yards farther than Devin's.
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