A boat travels at a speed of 20 mph in still water. It travels 48 miles upstream, and then returns to the starting point in a total of 5 hours. The speed of the current is ____mph?

I am not getting the setup right. Can someone help me?

The boat travel 48 miles in 5 hours

Therefore, the boat travel 48/5 = 9.6 miles/hour

Now in still water it can travel at 20 miles/hour, but is not going that fast, so the current must be acting against it.

If the current acting against it is (20-9.6) 10.4 miles/hour, then that explains why a boat at 20 miles/hour can only go 20-10.4 = 9.6 miles/hour.

I think that is how you answer this question.

Quote:

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Originally Posted by ceeters

A boat travels at a speed of 20 mph in still water. It travels 48 miles upstream, and then returns to the starting point in a total of 5 hours. The speed of the current is ____mph?

I am not getting the setup right. Can someone help me?

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For this problem, you need to use the variable R for the speed of the boat when it is traveling with the current.

Create two equations using Rate = Distance/Time

20 - C = 48/T
20 + C = 48/(5-T)

In case you're wondering, the T and 5 - T come from the fact that the trip upstream took T hours and so the time left for the return trip is 5 - T.

Using the addition method, you get:

40 = 48/T + 48/(5-T) Simplify by multiplying the whole thing by T(5-T)

You get:

40 (5T - T^2) = 48(5-T) + 48T

200T - 40T^2 = 240 - 48T + 48T

Two-step manipulation will get you:

40T^2 - 200T + 240 = 0 Divide by 40 you get:

T^2 - 5T + 6 = 0 which gives you (from factoring) T=2 and T=3

Plug that into your original equations and you will get C = 4

I think it's slightly easier to use Distance/Speed=Time. Knowing this you can set up a simple little equation
48/(20-C) + 48/(20+C)=5
where C is the speed of the current
Do some algebraic manipulations and you can solve for the speed of the current directly.

let speed of current be x miles / hr
speed of boat in upstream = (2o - x ) km / hr
speed of boat in downstream = (2o + x ) km / hr
speed = distance / time
time taken in upstream = 48 / ( 20 - x ) hr
time taken in downstream = 48 / ( 20 + x ) hr
accordind to question
48 / ( 20 - x ) + 48 / ( 20 + x ) = 5
on solving

x*2 - 16 = o
x = 4
speed of current = 4 miles per hour