Dakota runs a half-marathon every 6 weeks, and madison runs a half-marathon every 15 weeks. if they start now, in how many weeks will they again be running a half marathon at the same time?

30 weeks

Step-by-step explanation:

Given : Dakota runs a half-marathon every 6 weeks,

            Madison runs a half-marathon every 15 weeks

To Find : . If they start now, in how many weeks will they again be running a half marathon at the same time?

Solution :

Since Dakota runs a half-marathon every 6 weeks, Madison runs a half-marathon every 15 weeks

So, to calculate  If they start now, in how many weeks will they again be running a half marathon at the same time

We will take the LCM (lowest common factor) of 6 and 15

3 | 6,15

2 | 2,5

5 | 1,5

  | 1,1

LCM = 3*2*5 =30

The LCM of 6 and 15 is 30

So, If they start now, in 30 weeks they will again be running a half marathon at the same time

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct