PLEASE HELP

Question

A motorboat takes
5
hours to travel
100km
going upstream. The return trip takes
2
hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

distance = rate * time

b = boat speed

c = current speed

 

upstream distance = 100km

upstream rate = b - c

upstream time = 5 hours

downstream distance = 100km

downstream rate = b + c

downstream time = 2 hours

 

Two equations:

1) (downstream) d = r * t

  100 = (b + c) * 2

2) (upstream) d = r * t

  100 = (b - c) * 5

 

Simplify #1:

100 = (b + c) * 2

50 = b + c

 

Simplify #2:

100 = (b - c) * 5

20 = b - c

 

Algorithm:

Pick either simplification.

Solve for one of the variables.

Use substitution to solve for the other variable in the other equation.

Check your work.

 

I'll choose #2 to solve for b.

20 = b - c

20 + c = b

Now, I'll substitute the value of b into the other simplification to solve for c.

50 = b + c

50 = (20 + c) + c

50 = 20 + 2c

30 = 2c

c = 15

Now, I'll take the value of c and put it in the first equation to solve for b.

20 = b - c

20 = b - 15

35 = b

Check the work using the first equation:

1) 100 = (b + c) * 2

100 = (35 + 15) * 2

100 = 50 * 2

100 = 100

Check the work using the second equation:

2) 100 = (b - c) * 5

100 = (35 - 15) * 5

100 = 20 * 5

100 = 100

 

boat speed = 35 km/hr

current speed = 15 km/hr