Workout Part 3! word Problems

Hello, Brent!

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1. A car is scheduled to make a 616-mile trip in 9 hours.
The car averages 60 mph during the first 240 miles and 80 mph during the next 160 miles.
What must the average speed of the car be for the remainder of the trip
in order for the car to arrive on schedule?

This one doesn't require any fancy algebra.

The car drove 240 miles at 60 mph.
. . This took: . $\frac{240}{60} = 4$ hours.

The car drove 160 miles at 80 mph.
. . This took: . $\frac{160}{80} = 2$ hours.

It must drive $616 - 240-160 \:=\:216$ miles in the remaining 3 hours.

Its speed must be: . $\frac{216}{3} \:=\:72$ mph.

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2. The front and rear wheels of a buggy have radii of 14 inches and 30 inches, resp.
In traveling one mile (63,360 inches), what was the positive difference in the number
of revolutions made by the front and rear wheels?
Express your answer to the nearest whole number.

The circumference of a wheel with radius $r$ is: . $C \:=\:2\pi r$

The front wheel has a circumference of: . $2\pi(14) \:=\:28\pi$ inches.
. . In one mile, it makes: . $\frac{63,\!360}{28\pi} \:\approx\: 720$ revolutions.

The rear wheel has a circumference of: . $2\pi(30) \:=\:60\pi$ inches.
. . In one mile, it makes: . $\frac{63,\!360}{60\pi} \:\approx\:336$ revolutions.

The difference is: . $720 - 336 \:=\:384$ revolutions.

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3. Rex runs one mile in 5 minutes, Stan runs one mile in 6 minutes
and Tim runs one mile in 7 minutes. There are 5280 feet in one mile.
By how many feet does Tim trail Stan at the moment that Rex
completes a one-mile run? Express your answer as a decimal to the nearest tenth.

We know that Rex ran the mile in 5 minutes.

Stan runs the mile in 6 minutes.
. . In one minute, he runs $\tfrac{1}{6}$ of a mile.
. . In five minutes, he has run $\tfrac{5}{6}$ of a mile.

Tim runs the mile in 7 minutes.
. . In one minute, he runs $\tfrac{1}{7}$ of a mile.
. . In five minutes, he has run $\tfrac{5}{7}$ of a mile.

The difference is: . $\frac{5}{6}-\frac{5}{7} \:=\: \frac{5}{42}\text{ mile} \:\approx\: 628.6\text{ feet}$