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? HELPP ASAP

Answer 1

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

When the boat is traveling upstream (against the current), its effective speed is b - c. When it is traveling downstream (with the current), its effective speed is b + c.

We can use the following two equations based on the distance, speed and time relationship:

1. Distance = Speed x Time

2. Speed = Distance / Time

Using these equations, we can write two equations based on the given information:

1. (b - c) x 5 = 315 (Upstream journey)
2. (b + c) x 7 = 623 (Downstream journey)

Simplifying these equations, we get:

1. 5b - 5c = 315
2. 7b + 7c = 623

Dividing both sides of equation 1 by 5, we get:

b - c = 63

Adding equation 1 and equation 2, we get:

12b = 938

Dividing both sides by 12, we get:

b = 78.17 km/h

Substituting b = 78.17 in equation 1, we get:

78.17 - c = 63

Solving for c, we get:

c = 15.17 km/h

Therefore, the rate of the boat in still water is 78.17 km/h and the rate of the current is 15.17 km/h.

Answer 2

Let's call the rate of the boat in still water "b" and the rate of the current "c".

When the boat is traveling upstream (against the current), its effective speed is slower, so we can use the formula:

distance = rate x time

to set up the equation:

315 = (b - c) x 5

Simplifying this equation:

b - c = 63

Similarly, when the boat is traveling downstream (with the current), its effective speed is faster, so we can use the same formula:

623 = (b + c) x 7

Simplifying this equation:

b + c = 89

Now we have two equations:

b - c = 63
b + c = 89

We can solve for "b" (the rate of the boat in still water) by adding these two equations:

2b = 152

b = 76

So the rate of the boat in still water is 76 km/h.

We can solve for "c" (the rate of the current) by substituting the value of "b" into one of the equations:

76 + c = 89

c = 13

So the rate of the current is 13 km/h.