Question

boat traveled downstream a distance of 60 mi and then came right back. If the speed of the current was 6 mph and the total trip took 4 hours find the average speed of the boat relative to the water.

Answer 1

15 +√261 ≈ 31.155 mph

Explanation:

The time for the trip can be found by dividing the distance by the speed.

__

setup

The relation between time, speed, and distance is ...

time = distance/speed

The speed for the downstream leg was the sum of the boat speed (b) and 6 mph. The speed for the upstream leg was the difference. So the total trip time was ...

4 = 60/(b +6) +60/(b -6) . . . total time is the sum of the times for the legs

__

solution

Multiplying by the product of the denominators, we have ...

4(b +6)(b -6) = 60(b -6) +60(b +6)

b² -36 = 30b . . . . divide by 4 and simplify

b² -30b = 36 . . . . put in a form useful for completing the square

(b -15)² = 36 +15² . . . . . complete the square

b -15 = √261 . . . . . . . . take the square root (negative root is extraneous)

b = 15 +√261 ≈ 31.155 . . . . add 15

The average speed of the boat was about 31.155 mph.

Answer 2

7.5mph

Explanation:

Let the average speed of the boat to be x mph.

Total Distance = Avg. Speed x Total Time

60 = ((x+6) + (x-6))(4)

60 = (x+6+x-6)(4)

(2x)(4)=60

2x=60/4

2x = 15

x = 15 /2

x = 7.5mph