Question

A motorboat travels 315 kilometers in 5 hours going upstream and 623 kilometers in 7 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

Let's denote the rate of the boat in still water as 'b' and the rate of the current as 'c'.

We can use the following system of equations to solve for 'b' and 'c':

Upstream: 315 = (b - c) * 5
Downstream: 623 = (b + c) * 7

Simplifying the equations:

Upstream: b - c = 63
Downstream: b + c = 89

Adding the two equations together eliminates 'c':

2b = 152

Solving for 'b':

b = 76

Substituting 'b' into one of the original equations to solve for 'c':

b - c = 63

76 - c = 63

c = 13

Therefore, the rate of the boat in still water is 76 km/h and the rate of the current is 13 km/h.


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