4meonly wrote:I do not understand how you got this equation...
gaggleofgirls wrote:
then he rust have run 20/4 * 15 yards
Please help
I'll let gaggleofgirls explain her method. In the meantime, you might consider another (albeit slightly longer) approach to this question:
The important thing to recognize here is that the ratio of speeds between different pairs of people will be the same as the ratio of the distances they cover over a certain time. So, for example, in the race between Sharon and Rick, we see that Sharon runs m yards in the same time that Rick runs m-15 yards. So, we can conclude that the ratio of Sharon’s running speed to Rick’s running speed is m : m-15
Using this idea, we can conclude the following ratios of speeds:
(1) Sharon : Rick = m : m-15
(2) Rick : Christine = m : m-20
(3) Sharon : Christine = m : m-31
It will be useful to create an equation with this information. We can use ratios (1) and (2) to create a ratio between Sharon’s and Christine’s speeds. This new ratio must equal ratio (3). This will be our equation to solve.
We get (1) Sharon : Rick = m : m-15 = m^2 : (m-15)m
(2) Rick : Christine = m : m-20 = (m-15)m : (m-20)(m-15)
From here, we can conclude that Sharon : Christine = m^2 : (m-20)(m-15)
But this must equal (3)
So we get: m^2 : (m-20)(m-15) = m : m-31
We can solve this for m to get m=75 (answer choice A)
Brent Hanneson - Creator of GMATPrepNow.com
