Given the time taken by the boys in a relay race.
First, make the denominator of the given time of all boys to 12.
Time took by James
[tex]\begin{gathered} =\frac{2}{3} \\ =\frac{2}{3}\cdot\frac{4}{4} \\ =\frac{8}{12} \end{gathered}[/tex]Time took by Gilbert = 11/12
Time took by Matthew
[tex]\begin{gathered} =\frac{5}{6} \\ =\frac{5}{6}\cdot\frac{2}{2} \\ =\frac{10}{12} \end{gathered}[/tex]Time took by SImon = 7/12
1. In the given time, fastest boy is Gilbert (time with highest numerator) and the slowst boy is Simon ( time with lowest numerator).
The difference between the fastest boy's time and the lowest boy's time
[tex]\begin{gathered} =\frac{11}{12}-\frac{7}{12} \\ =\frac{11-7}{12} \\ =\frac{4}{12} \\ =\frac{1}{3} \end{gathered}[/tex]2. Time taken by the boys for the relay race equals the sum of time each boy taken. So. time taken for the relay race
[tex]\begin{gathered} =\frac{8}{12}+\frac{11}{12}+\frac{10}{12}+\frac{7}{12} \\ =\frac{8+11+10+7}{12} \\ =\frac{36}{12} \\ \end{gathered}[/tex]School record time for the relay race
[tex]\begin{gathered} =2\frac{7}{12} \\ =\frac{2\cdot12+7}{12} \\ =\frac{31}{12} \end{gathered}[/tex]Since 36 > 31, so the boys taken more time than the school's record.
Time slower were the boys than school record
[tex]\begin{gathered} =\frac{36}{12}-\frac{31}{12} \\ =\frac{36-31}{12} \\ =\frac{5}{12} \end{gathered}[/tex]The boys are 5/12 units slower than the school's record.
3. Given that:
Gallons of water the boys have to share that day
[tex]\begin{gathered} =4\frac{5}{6} \\ =\frac{4\cdot6+5}{6} \\ =\frac{29}{6} \end{gathered}[/tex]Gallons of water James drank
[tex]\begin{gathered} =1\frac{1}{3} \\ =\frac{3\cdot1+1}{3} \\ =\frac{4}{3} \\ =\frac{8}{6} \end{gathered}[/tex]Gallons of water Gilbert drank = 5/6
Gallons of water Matthew drank
[tex]\begin{gathered} =1\frac{1}{2} \\ =\frac{1\cdot2+1}{2} \\ =\frac{3}{2} \\ =\frac{9}{6} \end{gathered}[/tex]Gallons of water Simon drank
[tex]\begin{gathered} =\frac{2}{3} \\ =\frac{2\cdot2}{3\cdot2} \\ =\frac{4}{6} \end{gathered}[/tex]Total gallons of water the boys drank
[tex]\begin{gathered} =\frac{8}{6}+\frac{5}{6}+\frac{9}{6}+\frac{4}{6} \\ =\frac{8+5+9+4}{6} \\ =\frac{26}{6} \end{gathered}[/tex]Gallons of water left at the end of the day
= Gallons of water to share by the boys that day - Total gallons of water the boys drank
[tex]\begin{gathered} =\frac{29}{6}-\frac{26}{6} \\ =\frac{29-26}{6} \\ =\frac{3}{6} \\ =\frac{1}{2} \end{gathered}[/tex]Hence, 1/2 gallons of water left at the end of the day.
