jane works north of her home. her husband Bob works east. they leave for work at the same time. By the time Jane is 7 miles from home, the distance between them is one mile more than Bobs distance from home. How far from home is bob?

Question

jane works north of her home. her husband Bob  works east. they leave for work at the same time. By the time Jane is 7 miles from home, the distance between them is one mile more than Bobs distance from home. How far from home is bob?

anonymous · Answer

theorem of pythagoras i would say

anonymous · Answer

7^2 + (x)^2 = (x+1)^2

anonymous · Answer

this produces the quadratic $$49 + x ^{2} = x^2 + 2x + 1$$

anonymous · Answer

x=24

anonymous · Answer

i dont understand quadratics =(

anonymous · Answer

u dont have to in this case as you may simply subtract x^2 from both sides and you get a linear equation in x which is then solved by subtracting one from both sides and dividing by 2

anonymous · Answer

i dont understand any of it =(

anonymous · Answer

pythagoras theorem states $$hypthenuse^2 = adjacent^2 + opposite^2$$

anonymous · Answer

can u see how their movements form a right angled triangle? draw it for urself

anonymous · Answer

i thought it was a +b=c

anonymous · Answer

pythagoras' theorem? no the sides are squared

anonymous · Answer

i dont understand. sorry

anonymous · Answer

start by drawing the problem. mark a dot on the page for their home and then take a line 7 north for janes movement.

anonymous · Answer

now go back to the dot and take a line east for the dot (length doesnt matter) let this line have length x

anonymous · Answer

ok

anonymous · Answer

now mark the positions of mary and bob by a dot. now join those two dots and let the length of this new line be x+1 because the question says the distance between them is one more than how far bob is from home

anonymous · Answer

ok

anonymous · Answer

now can you see the right angled triangle? the hypothenuse (longest side) has length x+1. apply pythagoras theorem to get $$7^2 + (x)^2 = (x+1)^2$$

anonymous · Answer

then solve for x

anonymous · Answer

7x to the 4th = 2x+2?? i dont know what im doing...im far from help

anonymous · Answer

i think you are confused between powers of a number and mulitplication$$(x+1)^2 = (x+1)(x+1) = x^2 +x + x +1 = x^2 +2x +1$$

anonymous · Answer

which is the right hand side, left hand side is just 49 + x^2

anonymous · Answer

omg
 49 +2x=2x??

anonymous · Answer

almost $$49+x^2 = x^2 + 2x + 1 \rightarrow 49 = 2x +1 \rightarrow 2x=48 $$

anonymous · Answer

hm

anonymous · Answer

verify the steps yourself to make sure u understand

anonymous · Answer

i dont

anonymous · Answer

49+x times x=(x+1)(x+1)

anonymous · Answer

yes correct

anonymous · Answer

only i dont know how to answer that 49x2=x2+1x+1?

anonymous · Answer

thank you for your help