A driver would have reduced the time it took to drive from home to the store by 1/3 if the average speed had been increased by 21 miles per hour. What was the actual average speed, in miles per hour, when the driver drove from home to the store?  Choose the correct choice from the following:  A) 36  B) 42  C) 45  D) 48  E) 51

Rationale: "let r be the original speed and let t be the original time . since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 21 r / 2 = 21 r = 42 the answer is b ."
Answer: B