Question

Robin and Dovey have four pet pigeons that they train to race. They release the birds at Robin's house and then drive to Dovey's to collect them. To drive from Robin's to Dovey's, because of one-way streets, they go 3.1 km north, turn right and go 1.7 km east, turn left and go 2.3 km north, turn right and go 0.9 km east, turn left and go 1.2 km north, turn left and go 4.1 km west, and finally turn left and go 0.4 km south. How far do the pigeons have to fly to go directly from Robin's house to Dovey's house? Round your answer to the nearest tenth. (HINT: draw a picture!) *

Answer 1

Let the north and east with a positive sign, so, the south and west are negative signs

Because of one-way streets, they go 3.1 km north, turn right and go 1.7 km east, turn left and go 2.3 km north, turn right and go 0.9 km east, turn left and go 1.2 km north, turn left and go 4.1 km west, and finally turn left and go 0.4 km south.

So, the resultant horizontal distance = 1.7 + 0.9 - 4.1 = -1.5 km

The resultant vertical distance = 3.1 + 2.3 + 1.2 - 0.4 = 6.2 km

So, the direct distance will be calculated using Pythagorean theorem :

So, the distance d =

`\begin{gathered} d=\sqrt[]{(-1.5)^2+(6.2)^2}=\sqrt[]{2.25+38.44} \\ \\ d=\sqrt[]{40.69}=6.37887 \end{gathered}`

Rounding the answer to the nearest tenth

so, the answer is : 6.4 km