Algebra word problems

Question

When you swim with the current, you can swim 20 miles in two hours. However, when you swim against the current it takes you four hours. How fast is the current running and how fast could you swim if there was no current?

Answer 1

Use distance (d) = velocity (v) times the time (t)

 

d = vt

 

v = velocity if no current

c = velocity of current

 

With the current:

 

(v+c)(2 hrs) = 20 mi

 

Against the current:

 

(v-c)((4 hrs) = 20 mi

 

Just solve 2 equations in 2 unknowns v and c:

 

2(v+c) = 20

4(v-c) = 20

 

Simplifying both equations, we get

 

v+c = 10

v-c = 5

 

Add the 2 equations and get

 

2v = 15

v = 7.5 mph

 

Then c = 10-v = 10-7.5 = 2.5 mph