This is a algebra time and distance problem asked by an anonymous user in the ask a question section which stated,

"A boat travels 10 km upstream and 10 km back. The time for the round trip is 10 hrs. The speed of the stream is 4 km/hr. What is the speed of the boat in still water? Can someone help? I need it as a decimal."

Answer Coming Soon!

## Tuesday, March 30, 2010

### Time and Distance Problem 12

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coming soon? its 2011.. where is the answer?

ReplyDeleteYeah... I spend about 2 hours trying to solve this problem before I realized it was unsolveable. There's no answer, at least not one that makes sense.

ReplyDeleteIf it takes 10 hours to travel 20km, that's an average of 2kph. With a current of 4kph, this would mean that you went -2 kph upstream and 6 kph downstream. That's 5 hours travelling at 6 kph downstream (30 km) and 5 hours travelling at -2 kph (-10 km) for a scenic trip of -10km.

I redid the problem with the same time but over a distance of 30 km each way, and ended up with the much more reasonable result of 8 kph at rest, with a 7.5 hour trip upstream at 4 kph and a 2.5 hour trip downstream at 12kph.

there is an answer for this kind of question there is no question that doesn't have an answer. use quadratic equation.

ReplyDelete10 km upstream and downstream at 4kmph stream with the total of 10hrs round trip.

10/(x+4)+10(x-4)=10

10x+40+10x-40=10x^2-160

20x=10x^2-160

quadratic

10x^2-20x-160=0

-b +- sqrt b^2 - 4ac / 2a

-20 +- sqrt [ 400 - (-6400) ] / 20

-20 +- 82.46 / 20

x+ = 3.123

x- = -5.123

since the positive is cannot be derived to the speed we will use the negative one and change it to positive.

so the speed of boat in still water is 5.123

lets check:

upstream;

5.123 - 4 = 1.123 so the speed on upstream is 1.123, hence t=d/r or 10/1.123 = 8.90 so the time on the upstream is 8.90 hrs or 8 hours and 54 minutes and 16 seconds

downstream;

5.123 + 4 = 9.123 speed on downstream,

t=d/r or 10/9.123 = 1.096 or 1.10 or 1 hour and

5 minutes and 44 seconds.

therefore the time on upstream is 8.90 hrs and the time for downstream is 1.10 hrs which is equal to 10hrs.

so the answer is 5.123