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# Algebra/Rate

Question
In 1940 a motorcycle was used to measure the speed of a fastball.  The motorcycle had a 10 foot headstart and passed the pitcher at 86 mph as the windup was started.  The ball won by 3 feet.  Calculate speed of the ball.  Thanks for your assistance.

I assume the ball and motorcycle are both traveling to home plate , which is 60.5 feet away from the pitcher.

86 mph = 126.133 ft per sec

Let t be the number of seconds it takes the ball to travel the 60.5 feet .

In t seconds , the motorcycle has traveled 60.5 - 10 - 3 feet , because it had a 10 foot head start and was 3 feet away from home plate when the ball got to home plate

So , in t seconds , the motorcycle travels 47.5 feet.

t = 47.5 / 126.133  = .3766 seconds

The ball travels 60.5 feet in .3766 seconds

The ball speed is thus

60.5 / .3766  = 160 .648 feet per second

In miles per hour , the ball speed is

109.533 mph
Questioner's Rating
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Algebra

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#### Socrates

##### Expertise

Any questions on High School Algebra, College Algebra, Abstract Algebra. I can help with word problems, solving equations, trigonometry, inequalities, Gaussian Elimination, Linear Algebra, groups, fields, you name it!

##### Experience

Ph.D. in Mathematics, specialist in Algebra. I have taught High School students and college students at three state universities.

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Mathematical Association of America. American Mathematical Society.

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Regular contributions to the problems section of the American Mathematical Monthly journal.

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B.S., M.S., Ph.D.