Question

If it takes Julie 40 minutes to bicycle 5 kilometers, 52 minutes for 7 kilometers, and 64 minutes for 9 meters how long did it take her to ride 1 kilometer

Answer 1

Answer:

Step-by-step explanation:

I'm going to assume the last part means to say 64 minutes for 9 kilometers

Let's treat these like points on a graph.  You'll only really be able to tell time from distance if they are in a linear relationship, so let' check that.  We are gonna take the slope between each point and if they are the same it's a linear relation.

Of course slope is (y2-y1)/(x2-x1)

(52-40)/(7-5) = 6

(64-52)/(9-7) = 6

(64-40)/(9-5) = 6

Didn't need to check the slope between the third and first since the slope between the first and second as well as the second and third were the same but figured I would to show.  Anyway, the same slope means it is linear so we can solve the question.

Easiest way is probably to make an equation and then solve.  to make an equation you use the formula y - y1 = m(x - x1) where (x1, y1) are one of the points you were given and m is the slope, which we found to be 6.  So let's use (5,40) as our point.  Also 5 has to be x and 40 has to be y since that's what we used for the slope formula above.  Could easily have sqapped the two before though.  

y - y1 = m(x - x1)

y - 40 = 6(x - 5)

y = 6x - 30 + 40

y = 6x + 10

So now we can just plug in to find a distance or a time.  Again x is distance and y is time.  We have distance so we plug that in.  

y = 6(1) + 10

y = 6 + 10

y = 16

So that means it takes 16 minutes to go 1 kilometer.

Let me know if this didn't help.