# algebra

posted by
**Reiny**
.

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

---------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