Question

A motorboat maintained a constant speed of 11 miles per hour relative to the water in going 57 miles upstream and then returning. The total time for the trip was 22.0
of the current.
The speed of the current is

Answer 1

Based on the calculations,  the speed of this current is equal to 8 miles per hour.

What is speed?

Speed can be defined as the distance covered by an object per unit of time. This ultimately implies that, speed can be measured in miles per hour (mph).

Mathematically, speed can be calculated by using this formula;

Speed = distance/time

How to calculate the speed of the current?

Let c represent the speed of the current. Thus, the downstream and upstream speed relative to land would be given by this mathematical expression:

Speed downstream = 11 + c.

Speed upstream = 11 - c.

Also, the total would be given by:

Total time = total distance/speed

Time upstream + time downstream = 22 hours

57/(11 - c) + 57/(11 + c) = 22

Multiplying by (11 - c)(11 + c), we have:

57(11 + c) + 57(11 - c) = 22(11 - c)(11 + c)

57c + 627 + 627 - 57c = 22(121 - c²)

1,254 = 2,662 - 22c²

22c² = 2,662 - 1,254

22c² = 1,408

c² = 1,408/22

c² = 64

c -= √64

c = 8 miles per hour.

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