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A motorboat can maintain a constant speed of 46 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 39 ​minutes; the return trip takes 30 minutes. What is the speed of the​ current?

Respuesta :

Using the relation between velocity, distance and time, the speed of the current is of 6 miles per hour.

What is the relation between velocity, distance and time?

Velocity is distance divided by time, that is:

v = d/t.

For the upstream trip, we have that:

46 - vc = d/(39/60)

46 - vc = d/0.65

d = 0.65(46 - vc)

For the return trip, we have that:

46 + vc = d/(30/60)

46 + vc = d/0.5

d = 0.5(46 + vc).

Since the distance is the same, we can solve for vc as follows:

0.65(46 - vc) = 0.5(46 + vc)

29.9 - 0.65vc = 23 + 0.5vc

1.15vc = 6.9

vc = 6.9/1.15

vc = 6.

The speed of the current is of 6 miles per hour.

More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569

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