Victoria V. answered • 10/05/17

Tutor

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Math Teacher: 20 Yrs Teaching/Tutoring Calculus, PreCalc, Alg 2, Trig

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.