@j>................K..................>[2M/3]
j = K / (2M/3) = 3K / (2M)
"On the outbound leg of K miles, young John walked at a brisk pace. On the way back, young John had to run and so doubled his pace. The entire trip took M hours. Express his rate on the outbound leg in terms of K and M."
Here are the pretty obvious equations I derived from that..
RoTo = K, RbTb = K, RbTb = RoTo, Rb = 2Ro, Tb + To = M
Alright, if anyone can please show me how to work this out, I'd seriously appreciate it. Thanks.
What exactly do you mean by "rate"? Do you mean his speed?
The trip consists of K miles out, and K miles back, a total of 2K miles. At the outbound leg, he travels at some speed v, and on the way back, he travels twice that, namely 2v.
Hence the time it takes for the out-trip is K/v, while the time it takes for the trip home is K/(2v). These two times add up to M, hence K/v + K/(2v) = M. Isolating v gives you v = 3K/(2M).