Question

Catherine is at the Supermarket, and knows that she is 50 yards from her school. The map on her phone shows that the school is \large \frac{3}{4} inch from her current location. If Catherine's current location is 3 inches from home on the same map, how far is Catherine from her home? a 112.5 yards b 200 yards c 250.5 yards d 150 yards

Answer 1

Answer: b 200 yards

Explanation:

Scaling

Real magnitudes can be scaled up or down to adapt to the size of a sheet of paper or the screen of a computer or phone.

Catherine knows she is 50 yards from the school and it's shown as a distance of 3/4 inch on her phone map.

We can calculate the scaling factor from the real distance to the map distance by dividing:

`\displaystyle (50)/((3)/(4))=(200)/(3)`

Now she sees that she's 3 inches from home on the same map. This is equivalent to a real distance of:

`\displaystyle 3\cdot (200)/(3)=200`

Catherine is 200 yards from her home.

Answer: b 200 yards