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
