These are very easy to set up with a "chart"

Question

---------Distance-----Rate---Time (D=RxT)

slow way --6x----------x-------6
fast way - 5(x+7)-----x+7------5

so 6x = 5(x+7)

6x=5x+35+
x=35

The speed on the slower trip was 35 mph, and on the return trip 42 mph

A consultant traveled 6 hours to attend a meeting. The return trip took only 5 hours because the speed was 7 miles per hour faster. What was the consultant's speed each way?

Let X = distance one way
V1 = speed going
V2 = V1 + 7 = speed returning
X/V1 = 6
X/V2 = X/(V1+7) = 5
Now you have two equations in two unknowns (X and V1)
X = 6 V1
X = 5 (V1 + 7)
0 = V1 - 35
V1 = 35 mph
V2 = 42 mph
X = 210 miles