Richard's average driving speed is 7 kilometers per hour faster than Gracie's. In the same length of time it takes Richard to drive 292 kilometers, Gracie drives only 264 kilometers. What is Richard's average speed?

Let Richard's speed be R

Let Gracie's speed be G

We use these formulas:

R=G+7

And the distance speed time relationship of

d=vt

where v is speed. Then we write an equation:

d=vt becomes

292=Rt. (Richard drives 292km in a time t at speed R)

The other equation is for Gracie:

264=Gt

Now use R=G+7 in the first equation to get

292 = (G+7) t

Solving both of these equations for t by dividing by the speeds gives

264/G=t

292 / (G+7) = t

Now, because they drove these distances in the same time, t, we can set these two equations equal because the t's that they are both equal to are the same value.

264/G=292 / (G+7)

To get the G's on one side of the equation we first cross multiply to get

292G=264 (G+7)

Multiply the 264 through the parentheses

292G=264G + 1848

Subtract 264G from both sides

28G=1848

Divide by 28 to get G, Gracie's speed

G=66.

Now recall

R=G+7

R=73 km/hr