Question

I am having trouble understanding how to even approach this question

Answer 1

Given:

One friend heads north 20 miles per hour.

Other heads East 50 miles per hour.

let r be the number of hours traveled.

After t hours the distance traveled by the first friend is

`\text{Distance 1=speed}* time`

Substitute speed=20 and time =t, we get

`\text{Distance1=20t}`

After t hours the distance traveled by the second friend is

`\text{Distance 2 =speed}* time`

Substitute speed=50 and time =t, we get

`\text{Distance 2 =}50t`

Using the Pythagoras theorem to find the distance between two friends.

Distance between two friends is

`\text{distance }^2=(20t)^2+(50t)^2`

`\text{distance }^2=20^2t^2+50^2t^2`

`\text{distance }^2=400r^2+2500r^2`

`\text{distance }^2=2900t^2`

Taking square root on both sides, we get

`\text{distance }=\sqrt[]{2900t^2}`

`\text{distance }=10\sqrt[]{29}t`

Hence the required distance is

`\text{distance }=10\sqrt[]{29}.t`