SOLUTION: After sailing 13 mi, a sailor changed direction and increased the boat's speed by 4 mph. An additional 17 mi was sailed at the increased speed. The total sailing time was 2 h. Find

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Question 1173839: After sailing 13 mi, a sailor changed direction and increased the boat's speed by 4 mph. An additional 17 mi was sailed at the increased speed. The total sailing time was 2 h. Find the rate of the boat for the first 13 mi.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52809)   (Show Source): You can put this solution on YOUR website!
.

Let x be the slower rate, in miles per hour.

Then the faster rate is (x+4) mph.


The time equation is


     +  = 2   hours.    (*)


The solution/(the answer) is absolutely clear (obvious):  x = 13 mph.    ANSWER



CHECK.   +  = 1 = 1 = 2 hours.   ! Correct !

Solved (mentally).

-----------

Alternatively, you can solve equation (*) by reducing it to a quadratic equation, if you want.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Let the speed for the first part be x; then the speed for the second part is x+4.

The time for each part is the distance, divided by the speed; the total time is 2 hours:



That equation is solved relatively easily with basic algebra.

However, if you take a moment to look at the numbers in the equation, you might be able to see almost immediately that x=13 works....

ANSWER: 13mph for the first 13 miles.

CHECK: 13/13 + 17/(13+4) = 1+1 = 2
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