A boat traveled downstream a distance of 90 mi and then came right back. If the speed of the current was 20 mph and the total trip took 6 hourscomma nbspfind th

Question

A boat traveled downstream a distance of 90 mi and then came right back. If the speed of the current was 20 mph and the total trip took 6 hours, find the average speed of the boat relative to the water.

Answer 1

Let's let r be the boat's rate and t be the boat's time downstream

 

When it traveled downstream the boat's rate was r+20, since it was going with the current. The time that it took is t.

 

Since the trip was 90 miles and d = rt, 90 = (r+20)t. We can solve for t and say t = 90/(r+20)

 

The trip back was against the current, so the boat's rate was r-20. The time for that trip was (6-t) since the whole trip took 6 hours, but it was still 90 miles.

 

The equation for the trip back is (r-20)(6-t) = 90

 

If we multiply this out, we'll get 6r-120-rt+20t = 90

We can get all the t variables on one side of the equation so the equation becomes 6r-210=rt-20t

Now we can substitute the value for t from the downstream trip

 

6r-210 = (r-20)(90/(r+20))

 

If we multiply everything out we get

6r²-180r-2400 = 0, or r²-30r-400 = 0

 

We can now solve for r and find that the value of r is 40