Word problem help please!!!!!!!!!!!!

Let's use the following:

d1 = 154 km
t1 = 7 hours
d2 = 156 km
t2 = 6 hours
w = wind velocity (rate)
v = velocity (rate) of the cyclist in still air.

distance equals velocity multiplied by time

d1 = (v - w)t1

154 = (v - w)*7 -----> 22 = v - w

d2 = (v + w)t2

156 = (v + w)6 -----> 26 = v + w

So we have two equations with two variables:

22 = v - w

26 = v + w

Among other methods, we can add the two equations:

48 = 2v -----> v = 24

The rate of the cyclist in still air is 24 km/h

w = 26 - v = 26 - 24 = 2

The rate of the wind is 2 km/h

In order to confirm the results, we put these values into the original equations:

154 = (v - w)*7 -----> 154 = (24 - 2)*7 = 22*7 = 154 (good)

156 = (v + w)6 -----> 156 = (24 + 2)*6 = 26*6 = 156 (good)

I hope this helps...