Question

Two bikers, Derek and Tina, start riding from the same location. Derek rides due west for x miles. Tina goes due south and covers one mile more than Derek covers. When both bikers stop, the distance between the bikers is two miles more than the distance covered by Derek. How far did each biker ride?

Answer 1

c- derek 3 tina 4

Step-by-step explanation:

Answer 2

Answer: Tina rides 4 miles and Derek rides 3 miles.

Step-by-step explanation:

Since we have given that

Distance covered by Derek in west direction be x

Distance covered by Tina in south direction be x+1

Distance between the bikers when they both stop is x+2

Since it forms right triangle, so we will apply "Pythagorus theorem":

`H^2=P^2+B^2\\\\(x+2)^2=x^2+(x+1)^2\\\\x^2+4x+4=x^2+x^2+1+2x\\\\x^2+4x+4=2x^2+2x+1\\\\x^2-2x^2+4x-2x+4-1=0\\\\-x^2+2x+3=0\\\\x^2-2x-3=0\\\\x^2-3x+x-3=0\\\\x(x-3)+1(x-3)=0\\\\(x+1)(x-3)=0\\\\x=-1,3`

Since distance can't be in negative sign, so we take x=3 miles

Derek rides 3 miles

Tina rides is given by

`x+1=3+1=4\ miles`

Hence, Tina rides 4 miles and Derek rides 3 miles.