## alice fox and basil cat are searching for a treasure they start at the old oak tree in the field of dreams and walk 240 m, each counting her

Question

alice fox and basil cat are searching for a treasure they start at the old oak tree in the field of dreams and walk 240 m, each counting her own number of steps. Basil cat takes 100 fewer steps than alice fox. find the length of alice’s step and the length of basil’s step if basil’s step is 20 cm longer than alice’s step

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6 months 2021-07-15T22:41:34+00:00 2 Answers 4 views 0

1. alice fox’s step is 3/5 m and basil cat’s step is 4/5m.

note: i will be using 1/5m instead of 20 cm to keep the units consistent

1. Set up table

| Step Length | # of steps | Distance

A   |    x                 |    240/x     |   240

B   |       x+1/5       |  240/x+1/5 |   240

2. set up equation

240/x  –  100 = 240/x+0.2

3. Multiply the bases to make it:

240x+48 – 100x^2 -20x = 240x

=    100x^2-20x+48=0

4. Use vieta’s theorem or quadratic equation to solve for x

x= 3/5, -4/5 but -4/5 doesnt work bc distance can’t be negative

5. plug back in

A   |    3/5

B   |       3/5+1/5

so: alice fox’s step is 3/5 m and basil cat’s step is 4/5m.