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?

Question

anonymous · Answer

avg speed = total distance / total time
given In the same length of time it takes Richard to drive 292 kilometers, Gracie drives only 264 kilometers
let the time taken be t
so Richard's avg speed, say Sr = 292/t
    Gracie's avg speed, say Sg = 264/t
but also given that Richard’s average driving speed is 7 kilometers per hour faster than Gracie’s
=> Sr = Sg + 7
=> 292/t = 264/t + 7
=> 292 = 264 +7t                      // we multiply with t ion both sides of eqn.
=> t = 28/7 = 4
therefore
  Richard’s average driving speed = Sr = 292/4 = 73 kilometers per hour