6. Rebecca went swimming yesterday. After a while she had covered one fifth of her intended distance. After swimming six more lengths of the pool, she had covered one quarter of her intended distance.
How many lengths of the pool did she intend to complete?
A 40
B 72
C 80
D 100
E 120
Solution
E We have $\frac{1}{4}-\frac{1}{5}=\frac{1}{20}$. So the six additional lengths make up $\frac{1}{20}$ of Rebecca's intended distance. So the number of lengths she intended to complete was $20 \times 6=120$.