A motorboat travels 385 kilometers in 7 hours going upstream and 455 kilometers in 5 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Rate of the boat in still water 73 mi/hr

Rate of the current 18 mi/hr

Step-by-step explanation:

Calculation to determine the rate of the boat in still water and the rate of the current

Let B represent the speed of the boat in still water.

Let S represent the speed of the stream

Speed upstream = B-S.

Speed downstream = B+S.

Using the equation for distance

Distance=Rate * Time

Upstream

(B-S)7 = 385

(B+S)5= 455

Simplify first:

B-S=385/7

B-S = 55

B+S=455/5

B+S = 91

Solve by elimination. Add the two equations.

2B=55+91

2B = 146

B=146/2

B = 73 mi/hr

Substitute this into either equation and solve for S.

B+S = 91

73+S = 91

S=91-73

S = 18 mi/hr

Therefore the rate of the boat in still water is 73 mi/hr and the rate of the current is 18 mi/hr

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