20. Ruth and Sarah decide to have a race. Ruth runs around the perimeter of the pool shown in the diagram while Sarah swims lengths of the pool.
Ruth runs three times as fast as Sarah swims. Sarah swims six lengths of the pool in the same time Ruth runs around the pool five times.
How wide is the pool?
A $25 \mathrm{~m}$
B $40 \mathrm{~m}$
C $50 \mathrm{~m}$
D $80 \mathrm{~m}$
E $180 \mathrm{~m}$
20. B Let the width of the pool be $x \mathrm{~m}$. Therefore the total distance Ruth runs is $5(2 \times 50+2 x) \mathrm{m}=(500+10 x) \mathrm{m}$. The total distance Sarah swims is $6 \times 50 \mathrm{~m}=300 \mathrm{~m}$. Since Ruth runs three times as fast as Sarah swims, $500+10 x=3 \times 300$. Therefore $10 x=400$ and hence $x=40$.