: Logan is driving a boat that has a speed of 18 mph in standing water (no current). She drives the boat up and down a river to pick up people on tubing trips. The boat travels 4 miles each way and it takes half and hour to complete the round trip. How fast is the current that helps the boat one way and slows the boat the other way.

the speed of the current is 6 mph

Step-by-step explanation:

Let x represent the speed of the current.

Logan is driving a boat that has a speed of 18 mph in standing water.

Assuming the current slowed down the boat while she was going up(upstream), it means that his total speed was (18 - x) mph

Also, if the current helped the boat while she was going down(downstream), it means that his total speed was (18 + x) mph

Time = distance/speed

The boat travels 4 miles each way. The time taken to travel upstream is

4/(18 - x)

Time taken to travel downstream is

4/(18 + x)

The round trip took 0.5 hour. It means that

4/(18 - x) + 4/(18 + x) = 0.5

Multiplying through by (18 - x)(18 + x), it becomes

4/(18 - x) + 4/(18 + x) = 0.5(18 - x)(18 + x)

4(18 + x) + 4(18 - x) = 0.5(18 - x)(18 + x)

72 + 4x + 72 - 4x = 0.5(324 + 18x -

18x - x²)

144 = 0.5(324 - x²)

144 = 162 - 0.5x²

0.5x² = 162 - 144

0.5x² = 18

x² = 18/0.5 = 36

x = √36

x = 6

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step-by-step explanation:

3

step-by-step explanation: