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12. Ellen is at a hydroplane boat show. Starting from 1.0 miles away, the boat drives toward her and then passes her. The boat travels at a constant rate of 70 miles per hour. The distance of the boat from Ellen is given by d 11.0-70. At what times is the boat 0.15 miles from Ellen? Calculate your answer in seconds.

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One approach would be to find an equation describing the progress of the boat in a straight line in Ellen's direction FROM ITS STARTING POINT.  The initial distance would be 1.0 miles, and the distance as a function of time would be d = 1.0 miles + (70 mph)x, where x is the elapsed time.  When would the boat be .85 miles from Ellen?

Set the above distance formula = to 0.85 mile:

0.85 mile = 1.0 mile + (70 mph)x

-0.15 mile = -(70 mph)x
            0.15 mile
x = ------------------ = 
        70 mph

When the boat starts out, its distance from Ellen is 1.0 mile.  The boat speeds towards Ellen at 70 mph.  We want to know how long it takes for the boat to cover 0.85 mile from its starting point, which would be 0.15 mile from Ellen in front of her.

distance = rate times time

Here the distance is 0.85 mile, and the rate is 70 mph.

The time required is then   0.85 mile
                                           ------------- = 0.0121 hour, or 
                                             70 mph
                                                          0.0121 hour (60 minutes / 1 hour), or

                                                           0.729 minute, or 
 
                                                            43.7 seconds 

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