4 hr upstream then 2 hr downstream. speed upstream was 12 mph slower than his speed downstream. If traveled a total of 48 ​mi how fast was traveled​ downstream?

Question

I am in math 065 and have tried figuring out this problem for days. Please help. The assignment is due tomorrow.

Answer 1

Hi Courtney.

 

Let me see if I understand.

 

It took 4 hours to travel upstream.  It took only 2 hours to travel downstream.  

 

Speed upstream = speed downstream - 12

 

I will call the downstream speed s.   So upstream speed is s-12

 

Traveled the same distance upstream as he did down?  

If so, then he went 24 miles each way.

 

distance = rate * time

 

downstream:    24 = s * 2

 

upstream:  24 = (s-12) * 4

 

 

I get that s = 12 in the top equation, but I get that s = 15 in the bottom equation.  Since the two equations do NOT give the same s,  we have set the problem up wrong.  I am wondering if he traveled different distances.   

 

So if the distance he traveled upstream was d, then the distance he traveled downstream would be 48 - d.

 

That makes our two equations:

 

Downstream:   48-d = s * 2

 

Upstream:  d = (s-12) * 4

 

 

These simplify to

 

48 = 2s + d

48 = 4s - d

 

Now if we solve this system of equations...

 

Add vertically and get

 

96 = 6s, so s = 16 miles per hour.

 

Plug this in and solve for d, and get that d = 16

 

Now see if it works in both equations:

 

48 = 2(16) + 16   YES

48 = 4(16) - 16   YES

 

So we have found that the distance he traveled up stream was 16 miles, and the distance he traveled downstream was (48-16) = 32 miles.

 

We found that  his downstream speed was 16 mph, so his upstream speed would have been 4 mph.